Position a rack in the upper third of the oven. Preheat the broiler to high.
Halve each grapefruit, then loosen the segments by cutting along the membranes with a paring or grapefruit knife. Drizzle 2 teaspoons of rum evenly over each half.
In a small bowl, combine the butter, sugar, flour, allspice, and salt. Using your fingertips, pinch the ingredients together until the mixture forms soft crumbs. Sprinkle the crumbs evenly over the cut grapefruits.
Place grapefruits on a broiler pan, and broil until the crumbs are lightly browned, bubbling, and shiny, about 7 minutes. Serve immediately or cooled slightly.
Serve these for dessert at either dinner or brunch.
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