Place the sugar, mint leaves, and a splash of club soda into a highball glass.
Muddle well to dissolve the sugar and to release the flavor of the mint.
Squeeze the juice from both halves of a lime into the glass, dropping one half into the glass.
Add the rum.
Stir well.
Fill the glass with ice cubes.
Top with club soda.
Garnish with the mint sprig.