It’s maybe for this reason that during lunch, she seems tense. Polite but not warm. There’s a rigidity to the way the sits upright throughout the meal, even after a glass of wine is poured, and our glasses clink.

She lists Palestine as the primary issue (the other two being animal welfare and refugees) that she cared about during the “excruciatingly difficult” time she sat in Parliament when prime ministers Julia Gillard and Kevin Rudd were at war, forcing MPs to choose between them.

Parke served as the member for Fremantle from 2007 until she retired in 2016. It also ended whatever hope she might have had of making a political comeback in 2019, running in the seat of Curtin, when comments she made about an Israeli soldier forcing a pregnant Palestinian woman to drink bleach were reported.

The then Labor leader, Bill Shorten, a staunch ally of Israel, swiftly cut her loose and the “star candidate’s” light was snuffed out.

Parke frequently hopes we’ll turn the conversation to her work on nuclear disarmament, but then goes back to the Israel-Gaza war even when I turn to our time in Canberra – me as a press gallery journalist and her as a sitting MP – AUKUS and geopolitics.

In her pre-politics career as an international lawyer with the United Nations, she worked in Kosovo and Lebanon. But in the early 2000s she lived in Gaza before Hamas was elected to run the Palestinian Authority in 2006.

“I don’t think there’s a single other Australian politician who can say that, and so I think I have some legitimate perspective to offer,” she said, describing it as her duty to speak up on the issue.

Now, she says, “I just feel so sad, scared for the people”.

Even as today’s Labor Party has increasingly become home to more MPs and members with pro-Palestinian sympathies, her views would make life difficult for the prime minister and foreign minister.

Israel is carrying out “collective punishment” against the Palestinian people in Gaza, she tells me, and Western media do not tell the whole story when it comes to the conflict as Hamas’ attack, which, while not justified, was not unprovoked as it occurred within the context of a decades-long occupation.

She rails against extremism on both sides, naming the Likud political party headed by Prime Minister Benjamin Netanyahu, but agrees Hamas has made it harder for the Palestinians’ Western supporters to advocate their cause. “I don’t think it’s helpful at all.”

But when directly asked if she classifies Hamas, a proscribed terrorist organisation in Australia, Britain and the US, as extremist, she says: “There are different wings of Hamas. There’s a political wing, there’s a military wing, there’s a social wing.”

She says extremists on both sides need to be ignored if a solution is to be found.

Parke’s 2½ years in Gaza helped shape her post-politics career more than two decades later. She remembers vividly attending a Hiroshima commemoration in 2002 at the Gaza Harbour where hundreds of Palestinian school-children made paper boats and lit them with candles, floating them on the water. She laments that Gazan children of today are the ones being killed and mutilated by bombs.

But Parke’s job now is to convince the world to sign up to abolish nuclear weapons.

There’s a brief smile and interruption to the heavy conversation when one of the very photogenic dishes arrives, and she reflexively grabs her phone to start snapping. I promise to send her the high-resolution photographs of the food that our photographer, Jenny Magee, is keenly capturing.

Ending the threat of nuclear war seems an impossible task given China and North Korea’s build-up of their arsenals, Russia’s threats to use the weapons against Ukraine, and Britain and US justifying their own weaponry as a vital deterrent against authoritarians using theirs.

Parke’s Swiss-based organisation lobbies governments to sign onto the UN Treaty on the Prohibition of Nuclear Weapons.

The Labor government, led by her former factional left ally Anthony Albanese, has still not signed up, despite the prime minister introducing a pledge to do so at Labor conference in 2018. The motion was seconded by Richard Marles, now deputy prime minister and defence minister.

She said Albanese could sign the document tomorrow: “I look forward to him announcing that Australia’s going to join this treaty.

“There’s a great deal of anxiety [in the region about AUKUS] … and the potential for it to lead to Australia acquiring or hosting nuclear weapons.

“So by signing the treaty, Australia would essentially be asserting its own sovereignty.”

Parke is confident Albanese will stick to his word but agrees he doesn’t govern like a leftie. “I wish Labor governments in general would have more courage to act on the principles.”

Parke says none of the governments that hold nuclear weapons engage with ICAN, but civil society within Western countries like the US, France and Britain do. In Russia and China, they do neither. “I wouldn’t expect North Korea to have a civil society.”

She believes Australia is not immune from the effects of a nuclear war, even a limited one, including its climate effects.

“We are not just talking about the incineration of hundreds of thousands, potentially millions of people,” she says, warning of the potential for a “nuclear winter” that would block sunlight and cause mass crop failure.

“Even a limited nuclear war, between say Pakistan and India, could kill 120 million people outright and put at least 2 billion people at risk of starvation because of a nuclear winter.”

AUKUS has increased the threat to Australia, she says. “And of course with all of our military entanglement that we’re having with the United States now, we’re making ourselves a target.”

Parke says she would not have supported AUKUS as a caucus member saying it would not stack up on a cost-benefit analysis and that no one has set out how to deal with the nuclear waste.

“Probably the biggest issue for me is the issue of sovereignty and enmeshing ourselves, entangling ourselves so closely with the US military in every way, makes us a bigger target and reduces our own voice.

“I think there needs to be a much greater public examination of the merits of it.”

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She doubts the AUKUS submarines are needed to deter China, saying the money would be better spent on housing and mitigating climate change. The general sense of “angst about the world” would be better served by diplomacy rather than the “military beating of the drums for war that we’re seeing in Australia”.

Parke speaks quietly, but there’s a sharpness, terseness even, when I ask if her views aren’t a little outdated, given the huge shift across the world recognising China’s increasing aggression.

“What’s your point, sorry?”

I point to the Chinese blasting water cannons at Filipino vessels in Philippines waters as an example.

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“Is there any suggestion that China is any threat to Australia?” Parke responds. “Where’s the evidence?”

She says the enormous, punitive tariffs Beijing imposed on Australian wine and barley producers and a ban on coal were “in response to particular things that Australia has done as well on the international stage – calling for an inquiry into the origins of COVID”.

“I’m not here to defend China,” she says. “We shouldn’t be making something seem worse than it is – it’s being hyped, totally.

“Most of what I have seen about China has been, yes they are very territorial when it comes to what they see as their own country and their own country’s boundaries, extremely so, but there’s no obvious intent to go further.”

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Beijing has been engaged in skirmishes with the Philippines in waters that an international court has ruled do not belong to China.

When this is pointed out, Parke says: “Those are all matters to do with what it sees as its own territorial integrity”, and adds that countries should not be picking and choosing which international laws they want to abide by, returning to where the conversation began.

“There is a large-scale violation of international law happening in the Middle East now,” she says.