Preheat the oven to 400°. Spray 2 (6-well) donut baking pans with baking spray with flour.
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 or a zip-top bag with one corner snipped off.
Pipe about ¼ 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 top as directed.
For the Toppings:
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 half 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.)
When the rest of 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.
Be sure to measure the flour correctly, or once baked, you might end up with dense donuts. The ideal way to measure flour is with a scale. If you don’t have one, then fluff your flour with a spoon, sprinkle it into your measuring cup, and use a knife to level it off.
Be careful not to overmix the batter when blending flour and buttermilk mixture. Overmixing the batter can cause the donuts to become tough.
It’s best to use room temperature ingredients. Bring the egg and buttermilk out of the fridge in advance. This prevents you from overmixing the batter and promotes even baking.
Avoid overfilling the donut pan, or you might end up with a domed top.
Did the tops of the donuts close up when baked? Use a small round cookie cutter or the end of a piping tip to cut the middle out.
If you want a really thick glaze like those 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.
I recommend using real vanilla extract instead of artificial extract for the best flavor.