Add watermelon chunks to a blender. Blend until smooth.
Strain the watermelon puree through a fine mesh strainer into a bowl to remove pulp.
Fill a cocktail shaker with ice. Add 4 oz of the strained watermelon juice, rum, lime juice, and simple syrup.
Shake vigorously for 15-20 seconds until well chilled.
Fill two Collins glasses with fresh ice. Strain the cocktail mixture evenly between glasses.
Garnish each glass with a small watermelon wedge and mint leaves.
Notes
Use ripe, sweet watermelon for the best flavor. Pick a melon that feels heavy for its size and has a yellow spot where it sat on the ground.Store extra watermelon juice in an airtight container in the fridge for up to 2 days. For a non-alcoholic version, replace the rum with coconut water or club soda.You can use light or dark rum based on your preference.