For the watermelon, use a melon baller or small cookie scoop to make 10 (about ¾-inch) melon balls. Set aside in a medium bowl. Using a big spoon to scoop up all the flesh. Measure out 9 ounces of flesh and transfer to a blender or food processor. Make sure all seeds are removed. (Enjoy the leftover flesh yourself!)
Add mint leaves, lime juice, and sugar into the blender. Blend until smooth. Taste and adjust with sugar and lime juice if needed. Add desired amount of rum, 1½ – 2 ounces. Blend until just combined.
Add ice cubes and the watermelon balls into the hollow watermelon bowl, pour in the mojito. Serve immediately.