Generously grease an 8x8-inch square pan or baking dish with oil.
In a large pot over medium heat, mix together the coconut milk and water. Add the glutinous rice. Bring to a simmer then turn heat to low and cover. Let it cook until all liquids are absorbed. The rice should only be almost cooked at this point.
¾ can coconut milk, 1 cup water, 2 cups glutinous rice - washed and drained
While waiting, make the ube halaya, by putting the ube, coconut milk, and evaporated milk on a large pan or pot and cook over medium heat until fork tender. Use immersion blender or potato masher or wooden fork to mash into a puree.
1 can coconut milk, ¾ can evaporated milk, 2 cups ube
Add the condensed milk and cook while constantly stirring until thick and smooth.
¾ can condensed milk
Add the half-cooked rice to the pan of ube halaya. Gently fold until completely combined. Transfer the rice into the greased pan and spread out evenly.
Mix all the ingredients for the custard in a bowl then pour this over the rice and bake at 180C for 15-25 minutes or until custard is cooked and turns golden.
¼ can condensed milk, ¼ can evaporated milk, ¼ can coconut milk, 2 pieces egg yolks, 1 tablespoon flour