Divide the mint leaves and sugar evenly among four glasses. Muddle them gently to release the mint oils.
Add the lime juice and green food coloring to each glass. Stir to combine the color evenly.
Pour 2 ounces of white rum into each glass and fill with ice cubes.
Top each glass with club soda and stir lightly to mix.
Garnish with a mint sprig and a lime slice before serving.