For the next 11 weeks, Parker's penchant for exotic cuisine must be tempered. Only one thing, or one man, is on the menu now.
There will be no repeat of Mike Tyson and Evander Holyfield's 'Bite Fight' when the 26-year-old faces Britain's IBF and WBA champion on March 31 in Cardiff.
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But the first ever clash of two reigning heavyweight titlists on these shores promises to be a ferocious collision of young, hungry and unbeaten fighters.
Away from the ring, however, Parker is a man of serene pleasures.
"I love playing instruments — I play the piano and I play the guitar,' he reveals. 'My favourite song on the guitar is probably Hotel California. On the piano I love playing love songs, church songs, a mixture of things."
But the heavyweight is rarely happier than when shopping for fresh food.
"I love raw fish,' he says. 'After winning the world title (against Andy Ruiz Jnr in December 2016) I bought my dad a boat — eight metres — and I've taken it out more than him!
"We got it not long ago, probably two months ago, and I've taken it out maybe 15-20 times. I love fishing. The last time I went fishing, last Friday, I caught a two-metre mako shark, a hammerhead shark, a kingfish (and) a snapper."
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Parker is a man of few words. But on the topic of his favourite pastime, the New Zealander discovers a newfound gift of the gab.
He remembers one particular trip when he headed out to sea alongside tourists from America and around the world.
As would become a regular occurrence during our half-hour conversation, the world champion then recalled with words and actions how he devoured a fish alive — to the incredulity of fellow passengers.
"They looked at me like I was a weirdo," Parker claims.
On another occasion, the 26-year-old helped himself to a selection of crickets, centipedes, spiders and scorpions.
After eating one raw fish in Samoa — against the advice of those around him — the fighter was left paralysed for three days, fearing his career was over.
Fortunately the WBO king made a full recovery and is now on the verge of the biggest fight of his career to date. "I've chased Joshua for a long time — a year and a half, two years — and the reason is because we believe he's a good fighter, he'll give us a good challenge and we believe we can beat him," Parker says.
When he walks to the ring on March 31, Parker will be more than 18,000km away from his native Auckland.
But the money-spinning showdown is a world away from his boxing beginnings under the tutelage of his father Dempsey, named after the great American heavyweight Jack.
"(When) I was probably three or four years old, my dad used to go overseas for work and he would come back with pads, a little punch bag and gloves," Parker remembers.
'He would give it to me and my little brother (John) and we used to punch it. He held the pads and would say: "Boys this is your destiny!"'
Eventually, Parker gave up his other sporting pursuits — rugby union, rugby league and volleyball — to focus on the hardest game. And in the gyms of south Auckland, he sought to follow in the region's rich sporting heritage.
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Both Jonah Lomu and David Tua — a former foe of Lennox Lewis — hailed from nearby. But Parker's heroes were from even closer to home. "To be totally honest it was my parents," he says.
Dempsey and Sala Parker emigrated from Samoa to New Zealand in search of a better life.
"Seeing the hard work they went through was really inspiring," their son says.
"Being a young boy and watching them work two or three different jobs a day shaped me to be the person that I am because seeing that example helped me to work hard and focus on what I'm trying to do."
After years of applying what he learned at home and in the gym, Parker has conquered the world. But the 6ft 4in (1.95m) fighter remains wary of his keenest critics — particularly when it comes to trash-talking opponents.
"Anything I say in the media, my mum will talk about it," he reveals. "So I'll say 'mum was this okay?' and she'll say 'son, you shouldn't have said this' or 'son be careful what you say next time'. I think my upbringing and the standards they instilled in me helped me become the person I am today.
"I know a lot of fighters tend to talk a lot and say this or that. If I have said something in the past, it's not because it's me. It's because it was a team effort because we all came up with a plan to attack someone but personally it's not my style."
That is a trait shared by Joshua and, at first glance, they are two fighters with much in common. Both are likeable out of the ring and unbeaten inside it. But their paths to the top could hardly have been more contrasting.
While Parker learned the sport as a toddler, AJ didn't lace gloves until his late teens. And while the IBF and WBA champion came through Britain's brilliant amateur set-up, Parker had to battle a chronic lack of money and opponents to reach the top.
"When I was 16 I was fighting guys who were about 20 and older and when I travelled the world representing New Zealand, they gave me no money for funding," he says.
"My parents had to take out loans to pay for trips to India, Singapore, my coach took out a loan to pay for me to go to Russia."
At one world junior championships in particular, a 19-year-old Parker had to travel to Azerbaijan with his Australian counterparts — such was the paucity of financial support available at home. Despite these difficulties, however, pursuing another career never crossed Parker's mind.
"I had many jobs — I worked at a newspaper company in New Zealand loading trucks, I worked at McDonald's, I worked at a place called Fletcher Steel in New Zealand making steel and making stands. But boxing was pretty much the thing that stole my heart," he says.
Those tougher times are fortunately behind him. He now trains in Vegas, a town synonymous with fighting. Sparring partners and inspiration are aplenty. But for the heavyweight king, Sin City brings other advantages.
"In New Zealand there are a lot of distractions. When I'm in Vegas, no one knows who I am," he says.
"I love Vegas, I love not being known, I love being given time to myself. I love being heavyweight champion of the world — it was a goal for myself and my dad and every time I fight I celebrate with my family. So it's a joy to be a champion but I also enjoy my time where I am left alone and I can do what I want."
Nevada also provides the chance to learn from the best.
"I've been to (Floyd) Mayweather's gym when he was fighting (Conor) McGregor. We met him, took some photos and watched him train," Parker says.
Critics will say nothing can prepare Parker for the rarefied atmosphere of the Principality Stadium. But there are also those who believe he will upset Joshua — including Tyson Fury.
The pair struck up an unlikely friendship, even performing the haka together after Parker beat Tyson's cousin Hughie last September.
"He's so fun, relaxed, chilled and cool to hang out with," Parker says. "I still consider him a champion because he didn't lose his belts to anyone and I think when he does come back, if I still have the belt or have a chance to fight him, I would love to fight him."
Fury could even play his own part in the March 31 showdown.
"I might give him a text and say: 'Bro do you want to walk in with me?' He may just walk in with me or he may just sit in the front and watch the fight. But I know I have a lot of support from Tyson which is pretty awesome."
No one, not even the self-styled Gypsy King, will be able to help Parker once the first bell rings, however. Not that he appears daunted by the brutal task ahead.
"I don't care if I win or lose, I just love the challenge of fighting someone like (Joshua). Champion against champion to see who the real champion is. There's no anger, no hate, no animosity. Everything is about fighting and being the best."