1. Chop mint leaves into very small pieces.
2. Stem and halve strawberries. Put in a food processor or blender with sugar, lime zest, lime juice, and chopped mint leaves; process until blended.
3. To serve, pour 1/3 cup strawberry mixture and 2/3 cup club soda into each glass; add ice and stir. Garnish with a lime wedge and mint sprig.