Peel and pit the white peaches, then cut them into small chunks.
In a blender, purée the peaches with the lemon juice until completely smooth. If your peaches are very sweet, you can skip the sugar. Otherwise, add to taste.
Strain the purée through a fine mesh sieve for a silky finish.
Spoon 2 tablespoons of the peach purée into each chilled champagne flute.
Slowly pour chilled Prosecco over the purée. Stir gently to combine.
Serve immediately with a peach slice garnish if desired.
Notes
For a truly authentic Bellini, use white peaches. If you can’t find fresh ones, a high-quality white peach purée (like Cipriani’s) can be substituted.