Instructions

• In a mixing bowl, stir together 1 cup warm milk (107–110°F), 2 ¼ teaspoons active dry yeast, and 1 teaspoon of the 2 tablespoons granulated sugar. Set aside 10 minutes until foamy.
• Add the remaining granulated sugar (the rest of the 2 tablespoons), ¼ cup melted butter (cooled), about half of the bread flour (from the 2–3 cups), and ½ teaspoon salt to the bowl. Mix on low to combine.
• Knead on low with a dough hook, adding the remaining bread flour 2 tablespoons at a time as needed until the dough pulls away from the sides of the bowl and gathers on the hook. Use a total of 2–3 cups bread flour as required—the dough should feel tacky but not sticky and leave a slight residue on your hands. Continue kneading for 5 minutes.
• Lightly grease a clean bowl with a small amount of vegetable oil, place the dough inside, turn to coat, cover with plastic wrap or a clean kitchen towel, and let rise in a warm spot until doubled in size, about 1–3 hours.
• After the first rise, turn the dough out onto a floured work surface and roll to 1/2 inch thickness. Use a 3 to 3 1/2 inch donut cutter to cut donuts and donut holes. Place pieces on a parchment-lined baking sheet lightly dusted with flour, spacing them apart.
• Cover the cut donuts gently with a clean towel or plastic wrap and let rise until puffed (about 30 minutes), but not quite doubled.
• Meanwhile, pour at least 3 inches of vegetable oil into a deep, heavy-bottomed pot and fit with a candy thermometer. Heat over medium until the oil reaches 375°F (a range of 360–380°F is acceptable; the temperature will fall when you add donuts).
• Fry 3–4 donuts at a time, turning once, about 30–45 seconds per side or until golden brown. Monitor and adjust heat to maintain the oil between 360–380°F. Remove donuts with a slotted spoon and drain briefly on paper towels or a cooling rack.
• To make the glaze, whisk together 2 cups powdered sugar, 2 tablespoons whole milk, and 1 teaspoon vanilla extract. If needed, add more milk a little at a time until the glaze is a bit thinner than white school glue.
• Dip the top of each donut into the glaze, place on a cooling rack to allow excess to drip and the glaze to set, and serve warm or at room temperature.