In the bowl of a standing mixer fitted with the dough hook attachment, mix together warmed milk (be sure it is not too hot) and granulated sugar.
1 cup whole milk, ⅓ cup granulated sugar
Sprinkle the yeast over the top of the milk mixture and let it sit for 5 to 10 minutes until the surface of the milk becomes slightly foamy.
2¼ teaspoons active dry yeast
Use the dough hook to beat the sourdough discard, softened butter, 2 eggs, and nutmeg until mixed.
½ cup heaping sourdough discard, 8 tablespoons salted butter, 2 large eggs, ½ teaspoon ground nutmeg
With the mixer turned on low speed, add the flour, one cup at a time until it is all incorporated.
3¾ cups all-purpose flour
Continue mixing on medium speed for 4-5 minutes or until the dough leaves the sides of the bowl and forms a loose ball around the hook.
Place the ball of dough into a large greased bowl, cover with plastic wrap, and set in the refrigerator for at least 1 hour, or even overnight.
When the dough has doubled in size and is cold, divide it in half and transfer the first half to a lightly floured board.
Roll the dough to ½-inch thick and cut out donuts with a 3-inch round donut cutter or two round cutters to form a donut shape.
Place the donuts and “holes” onto a parchment lined baking sheet, leaving room between each donut for rising.
Spray a sheet of plastic wrap with non-stick cooking spray and place over the sheet of donuts.
Repeat the rolling and cutting steps with the other half of the donut dough.
Set the trays of prepared donuts in a warm place to rise for about 1 hour. They should double in height or be noticeably puffy. When you press your finger into the donut, it should bounce back just slightly, but leave a small dent.
While the donuts are rising, begin heating shortening or vegetable oil for frying. Use a heavy-bottomed saucepan (a Dutch oven is preferred) and fill at least 4 inches deep with oil. Heat, monitoring the temperature with a food thermometer, until the oil reaches and maintains 375°F.
Place 1 to 2 donuts into the hot oil at a time and fry on each side for 1 to 2 minutes or until golden brown.
Remove donuts to a paper-towel lined sheet pan to drain.
Prepare the glaze by whisking together powdered sugar, milk, and a pinch of salt.
3 cups powdered sugar, ½ cup whole milk, Pinch salt
Dip donuts into glaze, flipping to cover both sides, then place on a cooling rack to cool and dry.