Preheat oven to 425°. Grease donut pan or spray pan with non-stick cooking spray.
In a large bowl, mix butter, oil and sugars until smooth.
Whisk in eggs one at a time until combined.
Add baking powder, baking soda, nutmeg and vanilla to mixture. Stir until combined.
Stir in flour alternately with the buttermilk, beginning and ending with the flour. Mix only enough to combined.
Using a spoon, fill doughnut wells 3/4 full with batter, Dough is slightly stiff. Use a toothpick to spread dough out to edges of individual donut wells.
Bake on center rack of preheated oven for 10 minutes. Donuts are done when they spring back when lightly pressed. Donuts will be pale and do not darken with baking, this is normal.
Remove pan from oven and allow donuts to cool slightly before inverting pan to remove.
Make the glaze by combining confectioners sugar, corn syrup, melted butter, milk, vanilla and salt in a small bowl. Mix thoroughly. If glaze is too thick, add additional milk 1 teaspoon at a time until desired consistency.
Add the coconut to a large skillet over low-medium heat. Cook, stirring constantly, until the flakes are mostly golden brown. Remove from heat and transfer toasted coconut to a dish to cool.
Dip slightly warm donuts in glaze and then toasted coconut. Press on coconut to help adhere to the glaze.
Place donuts on a cooling rack to allow glaze to set before serving.