Put the simple syrup, mint leaves, and lemon wedges into a cocktail shaker and muddle them until the lemons are broken down and the mint is fragrant.

Add the bourbon and fill the shaker with ice. Using a long cocktail spoon, stir vigorously until very cold.

Fill a rocks glass with ice and use a fine strainer to strain the drink into the glass.

Gently smack the mint sprig with your hands to release its oils and fragrance. Garnish the drink with the mint sprig and serve.