Instructions

• Measure 1 cup plus 2 tablespoons whole milk into a microwave-safe bowl or measuring cup. Heat in 30-second increments on high until the milk is warm but not hot (test with a fingertip—should feel warm, not uncomfortable).
• Stir 1/4 cup sugar into the warm milk until dissolved. Sprinkle 2 1/4 teaspoons active dry yeast over the milk, stir gently once or twice, then let the mixture sit undisturbed for 10 minutes (it should become foamy).
• In a small bowl, whisk 2 large eggs with the 10 tablespoons melted unsalted butter (melted and slightly cooled). In a separate bowl, whisk together 4 cups all-purpose flour and 1/2 teaspoon fine sea salt. Set both bowls aside.
• Fit an electric mixer with the dough hook. Add the egg/butter mixture to the mixer bowl. Turn the mixer to medium-low and, with the mixer running, pour in the yeast/milk mixture. Let the hook mix this for about 1–2 minutes to combine.
• With the mixer still on medium-low, add the flour mixture in 1/4- to 1/2-cup increments, allowing each addition to incorporate before adding more, until all the flour is added.
• Stop the mixer and scrape down the bowl and dough hook. Turn the mixer on medium-low and knead for 5 full minutes.
• Stop the mixer, scrape the bottom and sides of the bowl, then run the mixer on medium-low for an additional 30 seconds.
• Turn off the mixer and let the dough rest, undisturbed in the mixer bowl, for 10 minutes.
• Lightly oil a clean bowl. Transfer the dough to the oiled bowl, turning it gently to coat all sides with oil. Cover the bowl tightly with plastic wrap.
• Place the bowl in a warm, draft-free spot and let the dough rise until doubled in size, about 1 hour. (If your kitchen is cold or drafty, place the covered bowl in the oven with only the oven light on; do not turn the oven on.)
• After the dough has doubled, gently deflate it (press down once or twice to release large air bubbles). Cover and refrigerate the dough for at least 8 hours or overnight.
• The next day, turn the chilled dough out onto a lightly floured work surface. Roll the dough to a thickness of 1/4 to 1/3 inch.
• Using a 3-inch cutter, cut as many doughnut rounds as possible. Re-roll scraps as needed and continue cutting. Use a 1-inch cutter to cut the center hole from each round and to cut doughnut holes from the scraps.
• Place the cut doughnuts and doughnut holes on a lightly floured baking sheet, spaced so they are not touching. Cover the sheet with a clean tea towel and let rise in a warm place until visibly puffed and airy, about 1 to 1 hour 15 minutes.
• When the doughnuts are nearly finished rising, heat canola oil in a large, heavy-bottomed pot to 375°F (190–191°C). Use enough oil to give the doughnuts room to float freely (at least 1 quart is a good guideline). Keep a thermometer in the oil and do not allow it to exceed 380°F.
• Fry 1–2 doughnuts at a time (do not overcrowd). Gently lower each doughnut into the hot oil and cook about 1 minute per side, turning once, until golden brown. Doughnut holes will cook faster—about 30 seconds per side.
• Use a slotted spoon to remove fried doughnuts and holes, letting excess oil drip back into the pot. Transfer them to several layers of paper towels for initial draining. Wait about 5 seconds, flip each once more onto a clean part of the paper towels for another 5 seconds, then move the doughnut to a wire rack set over a rimmed baking sheet to catch drips. Repeat with remaining pieces.
• Let the doughnuts cool slightly while you make the glaze.
• Whisk together 3 cups sifted powdered sugar, 1/8 teaspoon fine sea salt, 1/2 teaspoon pure vanilla extract, and 1/2 cup milk until completely smooth.
• One at a time, dip each doughnut into the glaze so it is submerged about halfway; completely submerge the doughnut holes and remove with a slotted spoon. Allow excess glaze to drip back into the bowl, then place glazed doughnuts right-side up on the wire rack. The rimmed baking sheet will catch drips.
• Let the glaze set briefly, then serve the doughnuts warm if possible, or at room temperature.