Whisk the warm milk, yeast, and 1 Tablespoon sugar together in the bowl of your stand mixer. Loosely cover and allow to sit for 5–10 minutes until foamy and frothy on top.

Add the remaining sugar, the eggs, butter, vanilla, nutmeg, salt, and 2 cups (about 250g) flour. Beat on low speed for 1 minute. Scrape down the sides of the bowl with a silicone spatula as needed. Add remaining flour and beat on medium speed until the dough comes together and pulls away from the sides of the bowl, about 2 minutes.

Keep the dough in the mixer and beat for an additional 5-7 full minutes, or knead by hand on a lightly floured surface for 5-7 full minutes.

Lightly grease a large bowl with oil or nonstick spray. Place the dough in the bowl, turning it to coat all sides in the oil. Cover the bowl and allow the dough to rise in a relatively warm environment for 1.5–2 hours or until double in size.

When the dough is ready, punch it down to release the air. Remove dough from the bowl and turn it out onto a lightly floured surface. Using a rolling pin, roll the dough out until it is ½ inch thick. Using a 3–3.5-inch doughnut cutter, cut into doughnuts.

Line 1 or 2 baking sheets with parchment paper or silicone baking mats. Place doughnuts and doughnut holes on each. Loosely cover and allow to rest for 30 minutes as you heat the oil.

Pour oil into a large heavy-duty pot fitted with an oil thermometer. Turn stove on to medium heat. Heat oil to 375°F (191°C). Add 2–3 doughnuts at a time and cook for 1 minute on each side. Carefully remove with a metal slotted spatula or metal slotted spoon.

Whisk all the glaze ingredients together. Dip each warm doughnut into the glaze, making sure to coat both sides. Place back onto prepared rack, as excess glaze drips down. After about 20 minutes, the glaze will set.