Put the simple syrup, mint leaves and lemon wedges into a cocktail shaker and muddle them until the lemons are broken down. 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. Put the mint sprig in the palm of one hand and gently smack it with the fingers of your other hand (this releases the oils and fragrance). Garnish the drink with the sprig and serve.