Preheat your oven to 425 degrees F. Grease a donut pan with non-stick spray or butter.

In a large bowl, whisk together the melted butter, vegetable oil, granulated sugar, and brown sugar until smooth.

Beat in the eggs one at a time, mixing well after each addition.

Stir in the baking powder, baking soda, nutmeg, salt, and vanilla extract until evenly combined.

Alternately add the flour and buttermilk to the mixture, starting and ending with the flour. Stir just until combined; do not overmix.

Spoon the batter into the prepared donut wells, filling them about three-quarters full. The batter will be thick; use a toothpick to spread it evenly to the edges.

Bake on the center rack for 10 minutes, or until the donuts spring back when lightly pressed. They will be pale—this is normal.

Let the donuts cool in the pan for a few minutes, then invert the pan to release them onto a wire rack.

In a small bowl, whisk together the powdered sugar, corn syrup, melted butter, 1 tablespoon of milk, vanilla, and salt. If the glaze is too thick, add additional milk 1 teaspoon at a time until it reaches a drizzling consistency.

Toast the coconut in a large skillet over medium-low heat, stirring constantly, until it turns mostly golden brown. Transfer to a plate to cool.

While the donuts are still slightly warm, dip the tops into the glaze, then press into the toasted coconut so it adheres.

Place the glazed donuts on a cooling rack to set before serving.