In a medium/large mixing bowl add the softened butter, oil, and sugars, and mix using a hand mixer or whisk until smooth.
Add the eggs and beat until combined.
Add the nutmeg, baking soda, baking powder, salt, and vanilla extract. Mix until blended.
Slowly add the flour as well as the milk mixing as you go. Combine until fully mixed. The batter will be quite thick which is normal, but you can add a tablespoon of milk at a time if it is too thick to work with.
Lightly spray donut tins with nonstick cooking spray and place the batter in using a spoon, or piping bag. Filling the donut wells about ¾ full works well.
While the donuts are baking prepare the frosting/glaze.
In a small/medium mixing bowl and the melted butter, milk, vanilla, and confectioner sugar. Stir into a paste consistency.
Bake at 425 for 10 minutes and let cool in the pan for another 5 minutes before removing it to a cooling rack.
While the donuts are still warm dip each one face down into the bowl of glaze and tip back over and place on the cooling rack.
Video
Notes
I get 14 donuts out of this recipe using this donut mold.If you want the extra glaze to let the first round of glaze cool the warm the glaze in the microwave for 15 seconds and then dip again into the glaze mixture. You may have to double the glaze.