"A juicy way to wind down after a busy day, and a good way to use up ripe peaches. Made and named for my friend Deb on her birthday. The peach-basil syrup makes 2 1/2 cups, enough for 8 to 10 cocktails. It keeps in the fridge for up to 3 weeks."
Combine chopped peaches, sugar, water, and 3 sprigs basil in a small pot over medium heat. Simmer, stirring occasionally, until sugar dissolves, about 5 minutes. Cool syrup to room temperature, about 10 minutes. Discard basil sprigs.
Pour syrup into a Mason jar, seal, and refrigerate until completely chilled, about 1 hour.
Measure 3 fluid ounces of syrup and peaches into a cocktail shaker; muddle to break peaches up. Add 4 ice cubes, bourbon, and bitters; cover and shake vigorously until ice is mostly melted. Pour into a chilled 8-ounce glass; add remaining 4 ice cubes. Gently stir in sparkling water. Garnish with a peach slice and basil leaf.