I think this is best made just before serving, in front of your friends. Halve your peaches, remove their stones, then pop them into a liquidizer and blitz until smooth. Add a splash of water if needed and put the puree into a jug. If you don't have a liquidizer just use your hands to squeeze, mash and really push the peaches through a sieve so you get as much as possible of their wonderful flavour and the colour from their skins into the puree. You can get the puree as fine as you like, but I don't mind the thickness...it's quite rustic. Discard (or eat!) whatever is left behind in the sieve, then pour the Prosecco into the jug and gently mix together. Divide among six glasses right away, and top up with a little more Prosecco, if need be, and enjoy!
NotesThe spirit of the Bellini isn't exclusive to peaches - nectarines or berries are also lovely used in the same way. There could easily be a Bellini for every month of the year.