Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13 inch baking pan.
Cook the soaked rice over medium heat in a saucepan with the soaking water, 1/2 can of coconut milk, and white sugar, stirring constantly, until tender and thickened, about 20 minutes. Pour into the prepared baking pan.
Stir together the brown sugar, remaining 1/2 can of coconut milk, and coconut preserves in a small saucepan, and bring to a boil. Pour the mixture carefully over the rice.
Bake in the preheated oven until the topping thickens, about 25 minutes. Cool completely; cut into squares to serve.
