Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Cut around the edges where the fruit meets the peel of each grapefruit half to loosen the fruit. Sprinkle cinnamon and nutmeg over each half and top with coconut sugar. Place grapefruit halves on a baking sheet or in a loaf pan.
Broil in preheated oven until sugar is browned, about 7 minutes. Allow to cool at least a few minutes.