Place simple syrup and mint into a cocktail shaker. Lightly muddle about 5-7 times, making sure to not over muddle because the mint will start to taste bitter.
Pour in lime juice and rum. Top with ice and shake, shake, shake.
Using a cocktail strainer, strain into two tall glass filled with a few ice cubes.
Top both glasses with club soda.
Garnish with some lime wedges and enjoy!