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

Add the remaining sugar, 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 as needed.

Add the remaining flour and beat on medium speed until the dough comes together and pulls away from the sides of the bowl, about 2 minutes. If needed, add more flour, 1 Tablespoon at a time, until the dough pulls away from the sides.

Knead the dough in the mixer for an additional 5-7 minutes or by hand on a lightly floured surface for 5-7 minutes until it is soft and slightly tacky.

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

Punch down the dough to release the air. Turn it out onto a lightly floured surface and roll out until it is 1/2 inch thick. Cut into doughnuts using a cutter.

Line baking sheets with parchment paper or silicone mats. Place doughnuts and holes on the sheets, cover loosely, and allow to rest for 30 minutes.

Heat oil in a large pot to 375°F (191°C). Add 2–3 doughnuts at a time and fry for 1 minute on each side. Remove carefully and place on a cooling rack.

Whisk together the glaze ingredients. Dip each warm doughnut into the glaze, coating both sides. Place back on the cooling rack to set for about 20 minutes.