In a small saucepan over medium heat, combine the sugar, water and lavender.
Simmer the mixture while stirring until the sugar is dissolved, about 2-3 minutes.
Then, remove the saucepan from the heat and let the lavender steep in the liquid for about 15 minutes. Strain the liquid into a clean container, collecting and discarding the lavender solids.
Add the chopped peaches and lavender simple syrup to your blender and blend on high until completely smooth. Transfer the purée to a clean container and refrigerate until chilled.
For the bellinis, place about 2 tablespoons of the chilled peach-lavender purée into champagne flutes. Slowly fill with Prosecco.
Garnish with a sprig of fresh lavender, if desired. Enjoy immediately.