1. Combine first 3 ingredients and 1/4 cup water in a medium saucepan. Bring to a boil; boil 5 minutes. Let cool completely. Remove and discard rosemary.
2. Preheat broiler. Place grapefruit halves on a large foil-lined jelly-roll pan. Brush syrup generously over tops of grapefruit; sprinkle top of each grapefruit with 1 1/2 tsp. turbinado sugar. Broil 6 inches from heat 7 minutes or until sugar melts and begins to caramelize. Brush grapefruit with pan juices. Serve immediately.
For a more intense rosemary flavor, prepare syrup 1 day ahead. Do not remove rosemary sprig until just before brushing syrup on grapefruit.