homemade baked doughnut

I thought doughnut making would be a fun after school activity and it was!  The kids and I made some very traditional looking and tasting donuts.  My husband grabbed all sorts of interesting things from the pantry to make voo-doo type doughnuts.  These baked doughnuts aren't the same as fried but they're totally fun to make and a lot healthier.
Note:  I made a double batch so that's the recipe you'll find below.  It made 3 dozen doughnuts in Wilton donut pans.
Update 1/24/18:  My daughter and I made these for the treat bucket for Activity Days.  We omitted the nutmeg and used 1/2 teaspoon lemon extract instead.  We added 3/4 cup mini chocolate chips to the batter.  For the vanilla glaze we added some lemon extract and everyone agrees they were much better!

homemade baked doughnuts (King Arthur Flour.com)
1/2 cup butter, room temperature
1/2 cup vegetable oil
2/3 cup brown sugar
1 cup granulated sugar
4 eggs
1 tablespoon baking powder
1/2 teaspoon baking soda
1 teaspoon ground nutmeg (I may put use lemon extract instead next time)
1 1/2 teaspoons salt
2 teaspoons vanilla
5 1/3 cups all-purpose flour
2 cups milk

Preheat oven to 425 degrees.  Lightly grease doughnut pans.  In a large mixing bowl, beat together the butter, vegetable oil, and sugars until smooth.  Add the eggs, beating to combine.  Stir in the baking powder, baking soda, nutmeg, salt, and vanilla.  Stir the flour into the batter mixture alternately with the milk, beginning and ending with the flour and making sure everything is thoroughly combined.
Spoon the batter into the lightly greased doughnut pans, filling the wells to about 1/4" shy of the rim.
Bake for 9 minutes.  Remove them from the oven, and wait 5-7 minutes before turning them out of the pans and onto a rack.  Dip into a glaze and decorate with toppings of your choice.

easy vanilla glaze
2 1/2 cups powdered sugar
2 tablespoons light corn syrup
2 tablespoons melted butter
4 tablespoons milk or water
1 teaspoon vanilla extract
Mix until nice and smooth.

chocolate glaze
1 cup semisweet chocolate chips
4 tablespoons butter
2 tablespoons plus 2 teaspoons light corn syrup
1/2 teaspoon vanilla extract

Melt in a small sauce pan on low heat until nice and smooth.