Preheat oven to 350 degrees. Spray donut pan with nonstick cooking spray.
Combine flour, cornstarch, baking powder, baking soda, salt, and nutmeg in a large mixing bowl.
In a separate bowl combine eggs, melted butter, cream of coconut, and vanilla. Add brown sugar and mix thoroughly.
Add wet ingredients to dry ingredients. Stir until just mixed, it will be a thick batter.
Spoon batter into a large gallon ziploc bag. Cut off the corner with scissors.
Pipe the batter into the donut pan, filling about 2/3 full. DO NOT overfill!
Bake donuts for 10-12 minutes. Let donuts cool in pan for 2 minutes before transferring to a wire rack. Note: Donuts should come out of the pan easily, but if there is any resistance, run a toothpick or butter knife around the edge to loosen. Spread coconut in a single layer on a baking sheet. Toast/bake at 350 degrees for 5 minutes. At this point, the coconut will begin to brown quickly so watch it and stir every couple of minutes until it is golden.
Allow toasted coconut to cool then place in a blender and pulse a few times to break it up.
Whisk powdered sugar and cream of coconut together. It will be THICK. Add water, just enough to thin out the glaze to your liking.
Dip cooled donuts into glaze on both sides, allowing excess to drip off, then roll donuts in toasted coconut.
Place donuts on a wire rack. The glaze will set up quickly.