With a very sharp knife, cut a slice from the bottom and top of a grapefruit, cutting into the fruit. Stand the grapefruit up on a work surface, and slice off the peel and white pith in vertical slices, exposing the fruit segments (cut slightly into the fruit part). Use your knife to gently slice between the exposed white membranes, and loosen the grapefruit segments into a bowl. Pick out any seeds. Repeat with remaining grapefruit. Shake any droplets of juice into the bowl as you work.
Gently stir the brown sugar and vanilla extract into the fruit until the sugar has dissolved; spoon into a 1-quart baking dish. Beat the egg whites and sugar in a glass or metal bowl with an electric mixer on medium-high speed until the mixture forms soft, glossy peaks. Spread the fruit with the ice cream, and spoon the meringue on top of the grapefruit in decorative peaks and swirls.
Bake in the preheated oven until the meringue is golden brown, about 7 minutes.
