The meringue in this dessert is made with brown sugar, the classic topping for broiled grapefruit.
Preheat broiler, with rack in lowest position. Put the egg whites and salt in the bowl of an electric mixer fitted with the whisk attachment, and beat on medium speed until frothy, about 30 seconds. Raise speed to high, and add sugar 1 tablespoon at a time, beating until incorporated. Continue to beat until the egg whites hold stiff (but not dry) peaks, about 3 minutes.
Place grapefruit halves, cut sides down, on a large plate; let drain 2 minutes. Invert, and carefully cut between membranes to loosen segments completely. Spoon one-quarter of meringue onto each half, using the spoon to create swirls and peaks. Transfer to a baking pan. Broil, checking frequently, until meringues are browned, about 30 seconds. Serve immediately.
Note: The eggs in this dish will not be fully cooked, so it should not be prepared for pregnant women, babies, young children, the elderly, or anyone whose health is compromised.