Add the mint leaves and lime juice to a cocktail shaker.
Using a muddler, gently muddle the mint leaves to release their oils and flavor.
Add the coconut rum and cream of coconut to the shaker.
Fill the shaker with ice and shake vigorously until well chilled.
Fill a serving glass with fresh ice.
Strain the cocktail into the prepared glass.
Top with 3–4 ounces of club soda and stir gently to combine.
Garnish with additional fresh mint leaves and serve immediately.