Rinse rice and cook in rice cooker. In saucepan combine coconut milk and 1 1/4 cups of the brown sugar. Cook over medium heat stirring constantly until thickened, about 20 minutes. Preheat oven to 350 degrees F.
Put cooked rice into a large bowl. Reserving 1/2 cup of coconut mixture, stir remainder and remaining brown sugar evenly into hot rice. Put into pans that are prepared by greasing them. Top with reserved 1/2 cup of coconut milk mixture. Bake for 20 minutes the broil for 5 minutes to set topping. Cut into small pieces.