Place rice in a large bowl. Cover with cool water and soak overnight. Drain and rinse rice. Drain and set aside.*
Preheat oven to 350° F. Generously butter an oven safe 9x13-inch casserole pan.
Reserve ¾ cup of coconut milk. Pour remaining coconut milk and 1 ½ cups water in a large sauce pot. Set over medium heat and cook until mixture begins to simmer. Add drained rice. Stir often, making sure rice does not burn along the sides of the pot. Continue to cook over medium heat for 5-8 minutes until rice has soaked up most of the liquid.
Reduce heat and add 1 ½ cups brown sugar and salt to rice mixture. Continue to cook, another 5-8 minutes, stirring often. Taste a small amount of rice to check it is cooked through. At this point, the mixture should be thick and sticky. Transfer cooked rice mixture into prepared pan. Spread into an even layer.
In a small sauce pot, combine reserved coconut milk and remaining 1 cup brown sugar. Bring to a boil until sugar has dissolved. Remove from heat. Allow to cool slightly, 3-5 minutes, before gently pouring over rice mixture.
Bake for 1 hour, until brown sugar topping has thickened and is bubbling. Allow to cool slightly before serving. The caramel topping will be very hot.