Ina Garten's cinnamon baked doughnuts are baked using two doughnut pans (each with six doughnut wells), and take less than 40 minutes to prepare, start to finish. This recipe makes 12 baked doughnuts.
Preheat the oven to 350 degrees Fahrenheit, and grease two doughnut pans with a baking spray that contains flour. Sift 2 cups of flour along with 1 1/2 cups sugar, 2 teaspoons baking powder, 1 teaspoon ground cinnamon, 1/2 teaspoon ground nutmeg and 1/2 teaspoon salt into a large mixing bowl. In a small bowl, combine 1 extra large egg with 1 1/4 cups whole milk, 2 tablespoons of unsalted, melted butter and 2 teaspoons of pure vanilla extract. Slowly stir the wet mixture into the dry ingredients until they just become combined.
Pour the batter into the baking pans, filling each well about three-quarters full. Bake the doughnuts until golden, about 17 minutes, or until an inserted toothpick comes out clean. Let the doughnuts cool for five minutes before tapping the doughnuts out onto a sheet pan.
While the doughnuts cool, prepare the topping. Melt 8 tablespoons of butter in a wide pan or bowl. In a small bowl, mix 1/2 cup white granulated sugar with 1/2 teaspoon ground cinnamon. Put each doughnut first in the butter, flipping to coat both sides, then into the cinnamon sugar. Serve the doughnuts immediately.