In a small saucepan set over low heat, warm the milk and butter until butter is melted. Remove from heat and let sit for about 5 minutes, or until mixture is 110-120°F.
In the bowl of a stand mixer fitted with a dough hook, combine two cups of the flour with the yeast, salt, and sugar. Add the warmed milk mixture and the eggs and mix until combined. With the mixer on medium speed, add the remaining flour ¼ cup at a time until dough is thick but still slightly sticky to the touch. Continue to knead on medium speed until smooth and elastic, about 4-5 minutes. Place dough in a greased bowl, cover with plastic wrap, and let rise in a warm place until doubled, about 1 hour.
Gently punch down dough to release gases and let sit for about 5 minutes. On a very lightly floured surface, roll the dough out into a circle about ½ inch thick. Use a 3 or 3 ½-inch round cutter to cut dough into circles. Use a smaller cutter, about 1 inch, to cut out the doughnut holes. Place on a sheet pan lined with parchment, cover with plastic wrap, and let rise in a warm place until puffed, about 30 minutes.
Fill a heavy bottomed pan with vegetable oil at least 4 inches deep and place over medium high heat. Insert a thermometer and heat to 370°F.
When oil is hot, fry doughnuts in small batches until golden brown, about 2 minutes on each side, flipping halfway through. Remove doughnuts with a slotted spoon to paper towels to drain. Top doughnuts as desired.
For the Cinnamon Sugar:
Combine the granulate sugar and cinnamon in a small bowl. Dip hot doughnuts into the sugar, flipping them over until they are completely covered. Use a spoon if necessary. Serve immediately.
For the Vanilla Glaze:
Whisk together the sifted powdered sugar, 3 tablespoons of the milk, and the vanilla extract until smooth and no lumps remain. Add more milk as needed to reach a desired consistency. Dip tops of doughnuts into the glaze, then invert and place on a wire rack set over a sheet pan to catch any drips. Let sit 30 minutes to firm up before serving.
For the Chocolate Glaze:
In a small saucepan over medium low heat, warm the butter, milk, corn syrup and vanilla until the butter in melted, stirring until smooth. Add the chopped chocolate and stir until chocolate is smooth and melted. Remove from heat and add the sifted powdered sugar.
Dip tops of doughnuts into the glaze, then invert and place on a wire rack set over a sheet pan to catch any drips. Decorate with sprinkles, if desired. Let sit 30 minutes to firm up before serving.
Video
Notes
NOTES
Doughnuts are best the day they are made, but will keep in an air-tight container at room temperature for about 5 days.
Each topping recipe makes enough to cover the entire batch of doughnuts.
Nutrition information calculated with just cinnamon-sugar topping and is an estimate.