Place the glutinous rice in a large bowl and cover with cool water. Let the rice soak overnight. Drain and rinse the rice, then set aside.
Preheat your oven to 350°F (175°C). Generously butter a 9×13-inch oven-safe casserole dish.
Reserve ¾ cup of coconut milk. In a large pot, combine the remaining coconut milk and 1 ½ cups of water. Set the pot over medium heat and cook until the mixture begins to simmer. Add the drained rice and stir frequently to prevent sticking and burning. Continue cooking over medium heat for 5-8 minutes, until the rice has absorbed most of the liquid.
Reduce the heat to low and stir in 1 ½ cups of brown sugar and the kosher salt. Cook for an additional 5-8 minutes, stirring often, until the rice is thick and sticky. Taste a small portion to ensure the rice is fully cooked.
Transfer the cooked rice mixture into the prepared casserole dish, spreading it evenly.
In a small saucepan, combine the reserved ¾ cup coconut milk and the remaining 1 cup of brown sugar. Bring to a boil, stirring until the sugar has dissolved. Remove from heat and let cool slightly for 3-5 minutes before gently pouring the mixture over the rice in the casserole dish.
Bake the Biko for 1 hour, or until the brown sugar topping is thickened and bubbling. Allow the dish to cool slightly before serving, as the caramel topping will be very hot.