Mix all the ingredients (except the coconut) in a large bowl. Stir in the flaked coconut and mix well to combine. Let the mixture rest for 15 minutes.
Preheat the oven to 300F. Line the pan with mini muffin cups. Fill each to the top with the mixture and bake for 30 minutes.
Keep leftovers in an airtight container.
Notes
*Sweetened flaked coconut has more moisture and looks a little damp when you peek through the packaging. If you can only find the sweetened shredded kind, you may have to soak the coconut a little longer in the milk-egg mixture for the liquid to fully swell the coconut.