In a small bowl, combine sugar and ¼ boiling water, stirring until sugar dissolves. Stir in ¼ cup mint leaves. Let cool completely. Strain through a fine-mesh sieve, discarding mint leaves.
In the container of a blender, combine cooled mint syrup, diced cantaloupe, and lime juice; process until smooth. Strain mixture through a fine-mesh sieve.
Divide remaining ¾ cup mint leaves among 6 glasses. Using a cocktail muddler or a wooden spoon, bruise mint leaves. Pour 2 ounces rum in each glass.
Fill each glass with frozen cantaloupe chunks or large ice cubes. Divide blended mixture between glasses (about ⅓ cup each). Top each with about 6 ounces sparkling water. Garnish with mint sprigs and cantaloupe wedges, if desired.
Notes
CANTALOUPE ICE CUBES: Arrange 1-inch pieces of cantaloupe in a single layer on a rimmed baking sheet. Freeze until solid; transfer to an airtight container, and freeze until ready to use.
Recipe by Louisiana Cookin' at https://louisianacookin.com/minty-melon-mojitos/