Make the simple syrup. Combine sugar and water in a small saucepan. Bring to a boil over medium heat, stirring until the sugar dissolves. Remove from heat and let cool completely. Simple syrup will keep covered in the refrigerator for up to a week.

Muddle the mint. Using a cocktail muddler, muddle the mint and simple syrup in the bottom of a tall glass.

Add remaining ingredients. Add lime juice and rum and club soda. Stir well then fill the glass with crushed ice, doing your best to keep the mint at the bottom of the glass.

Enjoy! Top with mint sprig and enjoy.