With a sharp knife, cut both ends off grapefruit. Set grapefruit on end on a flat surface and, following the shape of the fruit, cut away and discard peel. Cut sections out from the fruit, leaving the membrane behind.
Preheat broiler. Arrange grapefruit sections in 4 shallow ovenproof dishes (such as individual gratin dishes). Sprinkle with brown sugar. Broil until sugar melts and darkens, about 5 minutes (watch carefully). Serve warm, with dollops of yogurt.
Note: Nutrition analysis is per serving.