Preparation Add simple syrup and 2 mint sprigs to a cocktail shaker and press with barspoon or back of a wooden spoon to release mint oils. Add rum and lime juice. Fill shaker with ice, cover, and shake vigorously until outside of shaker is very cold, about 20 seconds. Strain cocktail through a Hawthorne strainer or a slotted spoon into a tall Collins glass filled with ice. Top off with club soda; garnish with more mint.