Add peeled peaches, water, and honey to a blender. Blend until smooth.
Strain the peach mixture through a fine-mesh strainer to remove pulp.
Place thyme sprigs and peach puree in a small saucepan. Heat on low for 5 minutes.
Remove from heat and let cool completely. Then, remove thyme sprigs.
Fill each champagne flute 1/3 full with the cooled peach-thyme puree.
Top slowly with chilled prosecco, stirring gently with a bar spoon.
Garnish each glass with a fresh thyme sprig.
Notes
Store extra peach puree in an airtight container in the fridge for up to 3 days.The recipe makes 6-8 servings, depending on glass size.For a non-alcoholic version, replace prosecco with sparkling water or white grape juice.Frozen peaches work well when fresh ones aren't in season. Just make sure to thaw them completely before using.