In an electric coffee/spice grinder combine sugar, ginger, and vanilla and grind fine. Halve each grapefruit crosswise and run knife around each section to loosen membranes. Arrange grapefruits, cut sides-up, in a flameproof baking dish or baking pan just large enough to hold them in one layer and sprinkle with sugar mixture. Broil grapefruits about 1 1/2 inches from heat until sugar melts and tops begin to brown, 10 to 15 minutes.
Serve grapefruits at room temperature.