Put the mint and simple syrup in a large rocks glass.
Muddle the leaves and syrup by pressing them with a pestle or a wooden spoon until juicy and fragrant. Add the rum, orange juice, lemon juice, run and ice.
Cover with a cocktail shaker and shake vigorously, or stir, until combined and chilled, about 30 seconds. (In general, by the time the shaker mists up the drink is ready.)
Divide into 2 glasses and top each with 4 oz. club soda.