Preheat the oven's broiler and set the oven rack about 6 inches from the heat source.
Remove all visible seeds from the grapefruit and loosen sections from membrane with a sharp knife. Place grapefruit halves cut side up in a baking dish.
Stir the oats, brown sugar, cinnamon, and salt together in a small bowl; add the butter and mash with a fork to incorporate oat mixture into the butter. Spread about half of the butter mixture over the top of each grapefruit half.
Cook under the broiler until the topping is golden brown, about 10 minutes.