Place the peaches and sugar into a food processor and whizz until fine. Push through a sieve until you are left with a fine purée. Add a little extra sugar if it needs sweetening, or a squeeze of lemon if it needs a kick.
Transfer to an ice-cream machine and churn according to the manufacturer’s instructions; or place in the freezer for 2 hours before whizzing in the food processor until smooth then returning to the freezer until frozen solid, another 2 hours.
When you’re ready for your cocktail, place a scoop of sorbet into 4 chilled champagne glasses and spoon over the vodka. Very slowly pour over the prosecco (careful, it will bubble up), stir, and drink at once.