Hush-a-Bye Bellinis

Puree peaches, sugar, and lemon juice in a blender until smooth. Pass mixture through a fine sieve into a metal bowl. Freeze until firm, at least 6 hours.

Scrape granita with a fork until fluffy. Freeze until ready to use.

Fill 20 Champagne flutes halfway with Prosecco (you'll have some left over). Add 1 tablespoon liqueur to each. Top each glass with 1 tablespoon granita. Serve immediately.