Prepare the Strawberry Peppercorn Syrup by combining all ingredients in a saucepan and bringing it to a boil. Simmer for 15 minutes until thickened. Remove from heat, add thyme sprig, and let steep for at least 30 minutes. Strain the solids and let the syrup cool. Refrigerate for up to one week.
In the cocktail shaker, add all ingredients.
Fill with ice and shake hard for 8 seconds.
Double-strain the cocktail into a cocktail glass using a Hawthorne and fine strainer.
Top with prosecco and garnish with a fresh strawberry.