During the NHL’s All-Star Weekend last February, Tampa Bay Lightning star Steven Stamkos was eager to make scrapbook-worthy memories with his then-2½-year-old son, Carter.

“As an athlete, you never know when it’s going to be your last All-Star game, so I made a point of bringing him up there with me,” Stamkos told The Post of having Carter with him during a press conference. “It meant the world to me.”

The 32-year-old father of two got that and more: a tender moment with his offspring that delivered a 10 on the cuteness scale and a viral video that stole the show.

While sitting on his father’s lap, Carter repeatedly asked to ride the Zamboni, punctuating every request with a precocious and well-mannered “please.”

Stamkos acquiesced and excused himself from the microphone. “We do a pretty good job of making sure he says ‘please’ and ‘thank you’ all the time. Probably one of the reasons I did end up leaving the press conference and going was because he asked politely.”

And thus, Carter Stamkos became known as “the Zamboni kid.”

So when the NHL and the Zamboni Company were launching their first electric Zamboni ride-on toy, they tapped their most famous little fan to officially introduce it.

In an equally adorable video, Stamkos took Carter to his home ice at Amalie Arena in Tampa and surprised the now 3-year-old with his very own mini Zamboni.

An excited Carter hops on and drives around the ice while his father takes the wheel of the adult-sized ice resurfacer alongside him.

“I was joking that he has more endorsement deals than I do now,” said Stamkos, who calls his toddler an “expert Zamboni driver.”

“I knew he’d love it, and I still can’t get him off it around the house. He’s on it every day. We had to kick him out of the house and make him ride it outside for stretches because when his younger brother [10-month-old Chase] is napping, it makes a lot of noise. It’s pretty funny.”

The toy had been in development for decades until the iconic company found a suitable partner with manufacturer Kool Karz, which was able to meet Zamboni’s specifications. It’s an authentic replica featuring the Zamboni machine’s trademark horn sound, working headlights and a snow collection tank for storage. It retails for $349 and will be available on the league’s site and the NHL store at One Manhattan West (Ninth Avenue at 33rd Street).

Paula Cooney, a brand manager for the Zamboni Company, said there was a “pent-up demand” for the item. “We’ve had people from around the world inquire about a ride-on Zamboni machine toy, and we’re so excited to finally have found the right manufacturer to work with on this project.”

Stamkos, who has back-to-back Stanley Cup Championships and seven All-Star appearances, said this moment ranks up there with those accomplishments.

“Anytime you have kids, it puts a new perspective on your life. And my two boys mean the world to me. So anytime I can be involved with them, it’s going to be instantly at the top of my achievements. This is right up there for sure.”

On Tuesday, his team will kick off the season at Madison Square Garden against the New York Rangers, who they eliminated in the Eastern Conference Final en route to the Stanley Cup Finals last year, where they lost to the Colorado Avalanche.

“Anytime you play a team in the playoffs, especailly that late in the playoffs, it starts to create a rivalry. I’ve played two conference finals at MSG in my career, and lucky for me, I’ve been on the right side of both of them. It’s an amazing place to play. The fans are great. It’s a hostile environment . . . These schedule makers do things on purpose, so it will be an interesting night for sure.”

As for Carter’s future in hockey, Stamkos said his son can chose which path he wants to pursue.

“He is just starting to skate on the ice now and is doing a learn-to-skate program in Tampa,” said Stamkos, adding, “We’ll see if he gravitates more toward wanting to be on the ice or drive the Zamboni. He can do whichever he wants.”