Before making your cocktail, make sure to chill your cocktail glass. I like to add ice cubes to the glass while I make the drink.
Add the simple syrup and basil leaves to your cocktail shaker. Muddle the basil leaves. Do this for a couple minutes until the basil leaves are completely crushed.
Add ice to the cocktail shaker.
Add your gin and lime juice to the cocktail shaker. Shake all ingredients thoroughly.
If you were chilling your cocktail glass, remove the ice cubes. Pour the mixture into the cocktail glass and garnish with a few basil leaves.