Frozen Watermelon Cocktail

Arrange watermelon evenly on a baking sheet lined with parchment paper. Freeze until completely frozen, at least 2 hours or up to 12 hours.

Bring water and sugar to a simmer in a small saucepan over medium heat. Simmer, stirring occasionally, until the sugar has dissolved, about 2 minutes. Remove from heat and stir in mint. Let stand at room temperature, uncovered, for about 30 minutes. Pour the syrup through a fine-mesh strainer into a small airtight container. Cover and refrigerate for at least 1 hour (or for up to 2 weeks).

Transfer the frozen watermelon to a blender. Add ice, rum, lime juice, bitters and 1/4 cup of the chilled mint syrup. Process until smooth, about 30 seconds. Divide between 2 glasses; garnish with additional mint and/or lime wedges, if desired. Serve immediately.