Add the basil and simple syrup to the bottom of a cocktail shaker. Use the muddler to bruise the basil leaves and break up the stems a tad. Add the gin, lemon juice, and a large handful of ice to the shaker. Affix the lid and then shake vigorously for about 20 seconds.
Add a large ice cube to the rocks glass. Double strain the cocktail into the rocks glass and then garnish with a fresh basil sprig. Serve.
