Yeast-Raised Doughnuts

Ingredients

• 1 1/8 cup whole milk, warmed to 90°F
• 1/2 cup sugar
• 2 1/4 teaspoons active dry yeast
• 2 whole eggs, beaten, at room temperature
• 3/4 cup butter, melted and cooled
• 4 cups bread flour
• 1 teaspoon salt
• 2 quarts frying fat
• 1/4 cup whole milk
• 2 1/2 cups confectioner's sugar
• 1 teaspoon vanilla
• 1 pinch salt

Directions

1. In a small bowl, combine the warm milk with the sugar and stir well. Sprinkle in the yeast, stir again, and leave it alone for 5 minutes, until the surface starts to look foamy. In another bowl, mix the egg with the melted butter, then set that aside. Add the flour and salt to the bowl of a stand mixer. Pour in the milk mixture and run the mixer on low until the flour is moistened, then turn the speed up until the dough comes together and looks fairly dry. Turn the mixer back down, add the egg mixture, and continue mixing until it disappears into the dough. Increase to medium-high and knead for approximately 10 minutes, pausing as needed to clear the hook and sides of the bowl. You should hear the dough smacking against the bowl as it works. When it looks smooth and pulls into a very elastic dough, stop mixing. Lightly coat a large bowl with vegetable oil, tuck the dough inside, cover with plastic wrap, and refrigerate overnight.
2. The next day, dust your work surface with flour and place the chilled dough on top. Sprinkle flour over the dough, press it down, then roll it into an even 1/2 inch thickness. Flour your round cutters, and prepare 2 sheet trays lined with plastic or silicone mats. If your kitchen is not hot and humid, heat the oven on its lowest setting just to create a warm proofing spot, then switch it off. Cut the doughnuts with the floured cutters or a doughnut cutter, and transfer them to the prepared trays. Leave room between them, since they will grow as they proof. Move the trays to the warm, moist spot and let the doughnuts rise for 45 minutes to 1 hour, until they are very puffed and delicate when touched.
3. Set up the frying oil and glaze before you begin cooking. Put a large, heavy pot on the stove and clip or rest the thermometer in place. Add the oil and heat it over medium. You want the oil at 375 degrees F, and you need to stay nearby to manage the temperature and keep things safe. Place a cooling rack lined with paper towels beside the stove, and have tongs, spiders, chopsticks, or strainers ready for flipping and lifting the doughnuts. On a different burner, pour the milk into a small saucepan and warm it over low heat until it starts to steam. Take it off the heat, add the confectioner’s sugar, pinch of salt, and vanilla, and whisk until smooth. Transfer the glaze to a bowl, set that bowl over a small saucepan of water, and leave it there for later.
4. When the oil reaches 375 degrees F, lower in the doughnuts one at a time until you have 3 in the pot. Cook them for approximately 2 minutes, then turn them over and fry for an additional 2 minutes on the second side. If they seem to be browning too quickly, you can flip them sooner. Move the fried doughnuts to the prepared cooling rack. Pull one open to check that the inside is cooked; if it needs more time, return it to the oil to finish, and adjust the timing slightly for the remaining doughnuts. Fry the rest the same way, then let all of them cool.
5. For the glaze, set the saucepan of water with the bowl of glaze over low heat and stir until the glaze loosens into a thick liquid again. Take it off the heat, then carefully dip each doughnut into the glaze with your fingers. Set the glazed doughnuts on a clean cooling rack so the coating can dry. As it sets, the glaze will look more translucent. For the best flavor, serve immediately.