Preheat the oven to 375°F.
Grease a 9 x 13-inch casserole dish thoroughly.
In a large mixing bowl, combine the eggs, melted butter, cream of coconut, whole milk, and granulated sugar.
Whisk until the mixture is smooth and evenly combined.
Set the coconut custard mixture aside.
In a separate mixing bowl, combine the softened cream cheese, granulated sugar, and cream of coconut.
Beat with an electric mixer for approximately 2 minutes, or until the mixture is soft, smooth, and creamy.
Transfer the cheesecake filling to a piping bag or a zip-top bag.
If using a zip-top bag, cut a small opening from one corner.
Spread half of the dried bread cubes evenly in the prepared casserole dish.
Pipe or squeeze the cheesecake filling evenly over the bread layer.
Spread the remaining bread cubes over the cheesecake filling.
Slowly pour the coconut custard mixture over the bread, distributing it evenly across the dish.
Gently press the bread down to help it absorb the custard mixture.
Sprinkle the sweetened coconut flakes evenly over the top.
Bake for 45 to 50 minutes, or until the custard is set and the top is golden.
If the coconut flakes begin to brown too quickly, gently cover the top of the bread pudding with a sheet of foil.
Continue baking until the center is fully set.
Remove the bread pudding from the oven.
Allow it to cool slightly before serving.
Serve warm, at room temperature, or chilled.