Butter a 9x13 dish. Arrange bread cubes evenly in the dish. In a large bowl whisk the yolks, whole eggs, coconut milk, cream of coconut, salt, nutmeg and mace. Stir in 1 cup of the coconut flakes. Pour all over the bread cubes, pressing the bread gently to soak up the custard, pour rum and do the same. Let stand for 1 hour covered in the refrigerator.
Preheat oven 325. Sprinkle the top of the pudding with remaining 1/2 cup of coconut. Cover the baking dish with foil, poking a few holes in top to release steam. Put the baking dish into a roasting pan and pour hot water into the pan halfway up the sides. Bake until pudding is firm to touch about 1 hour 15 minutes. Remove foil and bake 15 minutes more if needed, mine usually does. Remove from water bath and cool completely. When cooled cover and refrigerate.
If wanted: Chocolate Sauce: 1 cup semi sweet chocolate chips and 1/2 cup heavy cream, microwave and whisk until smooth. serve warmed over cold pudding.