Step 1

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.

Step 2

Pour syrup into a Mason jar, seal, and refrigerate until completely chilled, about 1 hour.

Step 3

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.