The striker is already a huge hit with the fans, of course, with the greatly catchy chant about him taking delight in his nation’s cuisine being sung loud and proud at Molineux.
But Cutrone’s lasting impact will be more than a song.
The Italian will boldly refuse to let any defender he comes up against have an easy ride.
The former AC Milan star will score a fair amount of goals along the way as well.
Cutrone has not exactly blown the doors off in gold and black up to now.
He missed a glorious chance against Manchester City and spurned a few inviting opportunities in the Europa League defeat to Braga at Molineux.
And one goal in seven Premier League appearances does not exactly set your pulse racing.
However, basing my opinion on what he has produced so far, the 21-year-old’s time will come.
The big plus point about Cutrone is that while he has not been finding the back of the net at a regular rate, he has not been short of chances.
Yes, him not putting a few more away is worth a slight raise of the eyebrow, but it would be far more concerning if he was not getting into scoring positions.
Cutrone has started two league matches – at Everton and City – and got off three and two shots in those matches respectively.
Off the bench against Chelsea – the game in which he opened his account – he managed three shots as well.
The hard-working centre-forward is also one of Wolves’ most fouled players this season.
Only Adama Traore and Diogo Jota get hacked down more often.
Cutrone is certainly asking questions of the opposition, even though the end product has been lacking.
He is not the only Wolves forward to have endured a slow start to life in the top flight either.
It took Jota 14 games to get off the mark last campaign.
Raul Jimenez, who ended up impressing so much that he was snapped up permanently for a club-record £32million, only scored three in his first 14 league matches.
The response of Milan supporters upon hearing the news Cutrone had been sold to Wolves in a deal rising up to £20m spoke volumes too.
Former Rossoneri team-mate Raoul Bellanova – now at Bordeaux – said last month: “He gave so much to Milan and the fans have always loved him.
“I honestly didn’t understand the choice to send him away.”
Nuno Espirito Santo has also hailed Cutrone as a fighter who has added a new dimension to Wolves.
Sprinting around as if every match is his last, with passion pouring out of him, there is a lot to admire about the youngster.
And if Cutrone does indeed add those desired goals to his game, he has every chance of becoming a Wolves hero – not just a cult hero with a top-match chant about him.