Enjoy this sparkling cooler all summer long. Use the back of a wooden spoon to muddle the mint.
Process first 3 ingredients in a blender or food processor until smooth. (Yield should be about 2 cups.)
Muddle mint leaves against bottom and sides of a glass pitcher to release flavors. (Leaves will be bruised and torn.) Add club soda, rum, and peach mixture; stir to combine. Serve immediately over ice.
Great with fresh peaches