Add the mint leaves and sugar to a cocktail shaker with a splash of the lime juice, and muddle until the mint leaves are slightly broken down.
Pour in the rum, blue curaçao and fill the cocktail shaker halfway with ice. Shake well for at least 15 seconds (to make sure the sugar disperses evenly).
Pour the mixture into ice-filled glasses and top with a splash of club soda. Enjoy with a mint garnish.