Preheat the oven to 400°F. Spray two (6-well) donut baking pans with baking spray. (This is a non-stick spray that contains flour, designed for baking!).
In a large mixing bowl, whisk together the flour, sugar, baking powder, cinnamon, salt, and nutmeg.
In a separate bowl, whisk together the buttermilk, egg, butter, vegetable oil, and vanilla. Add the buttermilk mixture to the flour mixture, whisking until fully combined. Transfer the mixture to a piping bag.
Pipe about 1/4 cup donut batter into each well. Bake until donuts are puffed and lightly golden, about 8 to 10 minutes. Immediately invert onto a wire rack and coat with cinnamon sugar or vanilla glaze.
For the Cinnamon Sugar:
In a small bowl, whisk together sugar and cinnamon. When the donuts come out of the oven, let them cool for 2 minutes, then immediately toss them in cinnamon sugar. (If the donuts are too cooled and the sugar mixture is not sticking, brush lightly with melted butter then toss in the sugar mixture.)
For the Vanilla Glaze:
When the donuts are cooled completely, in another small bowl, whisk together the confectioners’ sugar, milk, and vanilla. Dip the cooled donuts in glaze and return to the wire rack. Immediately add sprinkles, if desired. Let stand until the glaze is set.
Notes
If you want a really thick glaze for those delicious, iconic donut-shop treats, make a very thick glaze with 3 to 4 cups of sugar and 2 to 3 tablespoons of milk. Spoon or pipe the glaze on the top of the donuts. It should slowly settle and slightly drip down the sides. Top with sprinkles before the glaze dries.
Storage: If you have leftover donuts, keep them for 1 week in an airtight container. Store the donuts in a single layer to keep the glaze from sticking to each other. You can reheat them in the microwave for 5-10 seconds. Keep the intervals short or the glaze will melt off.
Make-ahead: Baked donuts have the best texture when they are eaten the day they are made (or in the first 24 hours), so I don’t recommend making them multiple days in advance. If needed, make them the night before and serve them the next morning.
Can I freeze the donuts? Freeze the baked donuts without the glaze in a single layer on a lined sheet pan before transferring them to a freezer-safe bag for 2 to 3 months. Thaw them for a couple of hours at room temperature. Glaze them or warm them up in the microwave for a few seconds before coating them with sugar.