Granita can be made of any deliciously ripe fruit; here, the combination of aromatic peaches and prosecco make for a festive delight.
In a small saucepan, combine the prosecco, sugar, juice of 1 lemon, mint, and salt. Bring to a simmer and cook just to melt the sugar, about 2 minutes. Remove from the heat and let cool.
When the prosecco syrup has cooled, put it in a blender with the peaches and remaining lemon juice. Purée until smooth.
Pour into a wide, shallow metal pan so the mixture comes about 1 inch up the sides. Put in the freezer.
Once ice crystals begin to form around the sides of the pan, about 1 hour, scrape the granita with a fork to incorporate the crystals back into the slush. Keep freezing and scraping every ½-1 hour until the granita is completely frozen in light, fluffy crystals.