For the Dough:
- 1 cup whole milk, warmed to 115º
- 1 tablespoon sugar
- 2¼ teaspoons (¼ ounce) active dry yeast
- 3½ cups all-purpose flour, plus more for dusting
- 1 teaspoon kosher salt
- 2 eggs, plus 1 yolk, beaten
- 6 tablespoons unsalted butter, softened, plus more for greasing
- Vegetable oil, for frying
For the Glaze:
1. Make the dough: In the bowl of a stand mixer fitted with a dough hook attachment, mix together the milk, sugar and yeast. Let sit until the mixture is foamy, 15 minutes. Add the flour, salt, eggs and butter, and mix on medium speed until a smooth dough forms. Transfer the dough to a large greased bowl, cover with plastic wrap and proof for 1 hour.
2. After the first proof, the dough should have doubled in size. Punch it down in the bowl, cover with plastic wrap and allow to proof again for 45 minutes.
3. While the dough proofs for a second time, make the glaze: In a medium bowl, whisk all of the glaze ingredients together until smooth. Cover with plastic and set aside until ready to glaze.
4. Make the doughnuts: Heat 2 inches of vegetable oil in a 6-quart Dutch oven to 350º. On a lightly floured surface, roll out the dough to a ½-inch thickness. Using a 3½-inch ring cutter, punch out doughnuts, then, using a 1-inch ring cutter, punch out a hole in the center of each one. Reroll the scraps as needed to get 12 doughnuts.
5. Line a baking sheet with a wire rack. Working in batches, fry the doughnuts, flipping once, until golden brown and puffed, 1 to 2 minutes per side. Transfer the cooked doughnuts to the prepared baking sheet to drain.
6. While the doughnuts are still warm, dip each one in the glaze and return to the wire rack to let the glaze set for 5 minutes, then serve warm.