Preheat the broiler. Position an oven rack in the top third of the oven. In a small bowl, stir together the sugar and cinnamon. Halve each grapefruit. Using a pairing knife, cut around the edge of the grapefruit and between the segments.

Arrange the grapefruit halves on a baking sheet or broiler pan. Sprinkle the cinnamon-sugar mixture evenly over the grapefruit halves. Place under the broiler for about 5 minutes, until the sugar is golden brown and bubbly. Keeping the oven door open a bit will help prevent burning. Be sure to watch closely, the sugar will burn quickly.