Blend 1 tablespoon fresh basil leaves and lemon juice in a blender for 1 minute. Pour mixture through a fine wire-mesh strainer, discarding solids.
Combine Pimm's No. 1, 1 ounce (2 tablespoons) basil-lemon mixture, and Simple Syrup in an ice-filled cocktail shaker. Cover with lid; shake vigorously until thoroughly chilled (about 30 seconds). Strain into an ice-filled rocks glass. Garnish, if desired.