Preheat broiler and prepare a baking sheet by lining with foil.
Cut grapefruit in half and carefully slice each segment out and around the outside with a serrated knife for easy scooping once the grapefruit is done broiling. Place on baking sheet and sprinkle with ground ginger and brown sugar. If the grapefruit doesn't sit evenly a toothpick placed underneath can help even it out.
Place under the broiler for 3-7 minutes until the sugar is bubbly and maybe even starting to brown. How long the grapefruit needs to broil depends on how close to the broiler and how hot it is, so watch carefully. If desired, add a tiny pinch of salt to the top and enjoy while still warm.