Preparation

• Position a rack in the center of the oven, and heat the oven to 425°F. Lightly grease the cavities of two standard doughnut pans with nonstick spray.
• In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl using a hand-held electric mixer), cream the butter, oil, and sugars on medium speed until light and fluffy, 4 to 5 minutes. Add the eggs one at a time, mixing on medium speed to combine. Mix in the vanilla, and scrape the bowl well.
• In a medium bowl, whisk the flour, cocoa powder, baking powder, and salt. Add half of the flour mixture to the butter mixture, and mix on low speed until incorporated. Add half of the milk, and mix to combine. Repeat, adding the remaining flour until incorporated, then the remaining milk until the batter is smooth.
• Transfer the batter to a pastry bag or heavy-duty ziptop bag with a corner cut off. Carefully pipe batter into each cavity of the prepared pans, filling each cavity to just under the top rim. (You can also carefully spoon the batter into the cavities instead.)
• Bake the doughnuts until a toothpick inserted into the center comes out clean, 7 to 9 minutes. Cool in the pan for 5 minutes, then turn onto a cooling rack.

Finish the doughnuts

• If you’re finishing with sugar: do it just after unmolding, while they’re still warm: toss the doughnuts in confectioners’ sugar or cinnamon-sugar until well-coated.
• If you’re glazing the doughnuts: let them cool at least 10 minutes more before glazing. Place a wire rack over a baking sheet. Working one at a time, dip each doughnut top side down into the glaze, and lift up, allowing the excess to drip back into the bowl. Invert the doughnuts onto the rack, and let sit for at least 15 minutes to allow the glaze to set.
• If you’re glazing with thin glaze: Place the doughnuts on a wire rack over a baking sheet. Ladle the glaze over each doughnut, allowing the excess glaze to fall over the doughnuts and collect on the baking sheet. You can collect glaze from the baking sheet and reuse it, if needed.
• If you’re adding sprinkles or other toppings to glazed doughnuts: apply them while the glaze is still wet so that they stick (allow the thin glaze to set for 1 to 2 minutes before applying the toppings).
• To use multiple glazes: Coat the doughnut with the fruit, chocolate, caramel, or vanilla glaze. Let the glaze set up, about 15 minutes. Then drizzle a second glaze over the doughnut, or dip part of the doughnut into a second glaze. Note: The thin glaze won’t work for this effect.

Variation: Mini Doughnuts

• Grease three mini doughnut pans with nonstick spray (it’s OK to work in batches if you don’t have multiple pans). Pipe (or spoon) the batter into the prepared pans, filling them just over three-quarters full. Bake at 425°F until a toothpick inserted into the center comes out clean, 4 to 5 minutes. Cool in the pan for 5 minutes before inverting onto a cooling rack. Yields 72.