Mix together the ingredients for the coconut layer and set aside. Mix together the ingredients for the ube layer and pour it into a parchment lined baking dish.
Cover with aluminum foil and bake or steam (see "Cooking the mochi" section below) until the top of the ube layer has just set ~15 minutes.
Pour the coconut layer on top and continue to bake or steam for 30 minutes or until the mochi has completely set.
Let the mochi cool completely– either overnight or for at least 4 hours before remove it from the container and cutting.