In a chilled julep cup, add the mint leaves, granulated sugar, and water; gently muddle just until the leaves release fragrance, 10–15 seconds (do not shred).
Add the bourbon and stir to dissolve the sugar.
Pack the cup tightly with the crushed ice, stirring until the cup frosts, 10–15 seconds, and mound more ice above the rim to form a dome.
Slap the mint sprig between your palms and nestle it near the rim; position a short straw beside it and serve immediately.