Preheat the broiler and adjust the rack so the top of the grapefruit will be about 4 inches below the heat. Remove any seeds from the grapefruit. Use a grapefruit knife or a small, serrated knife to cut around the outer edge of the fruit and between the segments. Try not to pierce though the peel.

Arrange the grapefruit cut side up on a baking sheet with a rim. Spread 2 teaspoons of brown sugar over the top of each fruit. Divide the ginger in half and sprinkle the portions over each half.

Broil for about 5 minutes, until the tops begin to brown. Serve immediately.