Preheat oven to 425°F. Grease a 6-count donut tin with nonstick spray. Set aside.
In a large bowl, with a hand mixer, combine the softened butter, oil, and sugars, and beat until smooth.
¼ cup unsalted butter, ¼ cup vegetable oil, ½ cup brown sugar, ½ cup granulated sugar
Add the eggs and beat until combined.
2 large eggs
Add the baking powder, baking soda, salt, nutmeg, and vanilla extract. Mix until blended.
1½ teaspoons baking powder, ¼ teaspoon baking soda, ½ teaspoon kosher salt, 1½ teaspoons pure vanilla extract, ⅛ teaspoon ground nutmeg
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.
2⅔ cups all-purpose flour, 1 cup milk
Using a spoon or spatula, fill the donut wells about ¾ full. Bake for 10 minutes and let cool in the pan for another 5 minutes before removing to a cooling rack. Repeat with the remaining batter.
While the donuts bake, make the glaze. In a medium mixing bowl, add the melted butter, milk, vanilla, and powdered sugar. Stir into a paste consistency.
1¼ cups powdered sugar, 1 tablespoon unsalted butter, 1 tablespoon milk, ½ teaspoon pure vanilla extract
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.
If you want extra glaze let the first round of glaze cool and then dip again into the glaze mixture. You may have to double the batch and you can slightly heat the glaze to make it spread easier.