Cut the peeled peaches into chunks and add them to a blender.
Blend until smooth, then strain through a fine-mesh strainer to remove pulp.
Add lemon juice and sugar (if using) to the peach puree. Mix well.
Fill each champagne flute 1/3 full with the peach mixture.
Top slowly with chilled Prosecco, stirring gently to combine.
Garnish with a fresh peach slice.
Notes
Store extra peach puree in an airtight container in the fridge for up to 2 days.For best results, use yellow peaches that are ripe but still firm.White peaches can work as a substitute, though they create a milder flavor.Frozen peaches work in a pinch - thaw them completely before blending.Skip the sugar if your peaches are very sweet.Prosecco can be replaced with other sparkling wines, but true Bellinis use Prosecco.