Wash and peel the peaches, cut into wedges and place in a food processor. Purée until completely broken down. Add the sugar and mix again until blended.
Bring purée to boil over medium-high heat and cook (stirring occasionally), until it reduces to measure about a cup (approximately 236ml).
For the Bellini cocktails:
Pour the peach purée into a champagne flute (fill it about a third of the way). Gently pour ice-cold Prosecco to fill the glass.
Only stir when ready to drink.
Optional: Finish it off by adding some peach wedges to the glass.
The puree can be made two or three days in advance when stored in the fridge. Once ready to use, if it has become quite thick, just mix it with a little water. See the tips at the bottom of the post for making it last longer.