Jiro's mom was a assassin for the Yakuza, Jiro's dad was a hitman for the Italian "Family". 

A Yakuza crime boss came over from Japan to close a smuggling deal with the Family, and brought Jiro's mom along as part of his security team. At one of the crime boss’s dinner meeting's Jiro's mom ate an Italian dish that she absolutely loved! She had to compliment the chef. When she found out the chef was one of the Italian Family’s hitmen, it was love at first sight! 

It was a match made in hitman heaven. They got married and soon had a bouncing baby Jiro. The happy hitman family stayed on the Italian side, and Jiro quickly grew up to be the best of both worlds. He picked up his mom's love of blades and his dad's tankiness. And also his dad's love of cooking. 

Everything was going great for the lethal family, but when their adopted son Reise, Jiro’s best friend/little brother, was killed during a hit job everything changed. Jiro’s family was devastated. Jiro's parents decided to retire, and move back to Japan. And even Jiro chose to step down from his head hitman position. 

Without his brother by his side, Jiro's heart just wasn't in it any more. 

So he followed his passion and became a chef at one of the many Family owned restaurants. That is, until he was kidnapped and tortured to death, then turned into a zombie to try to get info from him by a rival gang.