Place the rum, grapefruit juice, mint leaves, lime juice and 4 ice cubes into a blender.
Pulse a couple of times until everything gets mixed up and the ice is roughed up a bit.
Evenly divide the brown sugar between 2 glasses.
Place 2-4 ripped up mint leaves on top of the brown sugar in each glass.
Drop 2 ice cubes into each glass on top of the mint leaves.
Fill each glass up with the cocktail mix from the blender and serve.