Add chopped peaches to a blender and blend until smooth.
Strain the peach puree through a fine-mesh strainer to remove pulp.
Fill each champagne flute with 2 tablespoons of peach puree.
Add 1 oz vodka to each glass.
Top with chilled prosecco, stirring gently with a bar spoon.
Garnish with a fresh peach slice.
Notes
The peach puree can be made ahead and stored in the fridge for up to 24 hours.Use ripe, yellow peaches for the best flavor. White peaches work too but may need extra simple syrup.For a non-alcoholic version, replace prosecco with sparkling water or white grape juice.Frozen peaches can replace fresh ones when peaches aren't in season.