Melt butter in a Dutch oven over medium-high heat. Add onion; sauté 4 minutes or until tender. Add rice, and stir until well-coated and translucent, about 1 to 2 minutes. Stir in brown sugar and next 3 ingredients. Stir in half of coconut milk. Cook, stirring constantly, until liquid is absorbed. Repeat with remaining coconut milk. Stir in the hot broth, 1 cup at a time, stirring frequently, until each addition has been absorbed. (The entire process should take 20 to 25 minutes.)
Stir in crabmeat and mango, and cook 3 minutes or until thoroughly heated. Sprinkle with flaked coconut.