Preheat oven to 425°F. Grease a 6-count donut tin with nonstick spray. Set aside.
In a large bowl, combine the cake mix, milk, vegetable oil, egg, vanilla, and nutmeg (if using). The batter should be quite thick, but add a little extra milk if it seems too thick to work with.
15.25 ounces vanilla cake mix, ¾ cup milk, ⅓ cup vegetable oil, 1 large egg, 1 teaspoon pure vanilla extract, ⅛ teaspoon ground nutmeg
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.