Glazed Doughnut Muffins

I let my 10 year old daughter make muffins and she choice this recipe found here at Sweet Pea's Kitchen. They were a big hit.

1/4 cup butter
1/4 cup oil
1/2 cup sugar
1/3 cup brown sugar
2 eggs
1 1/2 teaspoons baking powder
1/4 teaspoon baking soda
3/4 teaspoon nutmeg
1 teaspoon cinnamon
3/4 teaspoon salt
1 teaspoon vanilla
2  2/3 cups flour
1 cup milk
For the Glaze
3 tablespoons butter melted
1 cup powdered sugar
3/4 teaspoon vanilla
2 tablespoons hot water

1. Preheat oven to 425 degrees. Line 12 muffin cups with muffin liners. 
2. With a mixer beat butter oil and sugar until smooth. 
3. Beat in eggs one at a time.
4. Mix in the vanilla, baking soda, baking powder, nutmeg, cinnamon, and salt just until combined.
5. Stir the flour into the butter mixture alterating with the milk making sure everything is well mixed.
6. Divide batter into the 12 muffin cups. 
7. Bake until muffins are a pale golden about 15-17 minutes.
8. Cool muffins in muffin tins for 5 minutes, then transfer to wire rack and cool 10 minutes before glazing. 
9. To make the glaze, in medium bowl mix the melted butter, powdered sugar, vanilla and water. Whisk until smooth.
10. When the muffins have cooled, dip the muffin crown into the glaze and allow the glaze to harden. Once harden dip a second time and allow to harden and serve.