In the bowl of an electric mixer, combine 4 cups flour, granulated sugar, nutmeg, cinnamon, and yeast. Whisk to evenly combine.
5 cups all-purpose flour, ¼ cup granulated sugar, ½ tsp ground nutmeg, ½ tsp ground cinnamon, 2 ¼ tsp (1 pkg) instant yeast
Pour the milk into a small saucepan and heat over medium heat on the stovetop. When the milk begins to steam, but not boil, remove from heat and add the butter. Stir until the butter is melted and the mixture registers 110-115°F. Whisk in the vanilla extract and eggs and pour into the prepared flour mixture.
⅓ cup unsalted butter, 1 ¾ cups whole milk, 1 tsp vanilla extract, 2 large eggs
In the bowl of a stand mixer, mix on low with a dough hook attachment until a shaggy dough is formed. Turn to medium and mix for 3 minutes.
Add the salt and then slowly add the remaining 1 cup of flour as needed until a smooth dough is formed, leaving the sides of the mixing bowl clean.
2 tsp kosher salt, 5 cups all-purpose flour
Lightly flour a work surface and knead the dough by hand to ensure it is smooth and elastic. Place dough into a well-oiled bowl and cover. Set in a draft-free location until doubled in size, about 1 to 1 ½ hours. Personally, I use my oven with the oven light on to raise the dough.
Once doubled, roll out dough on a floured surface to ½-inch thickness. Cut donuts with 3-inch and 1-inch round cutters. Any size can be used.
Place donuts and donut holes on a parchment-lined baking sheet sprinkled with flour, leaving at least 2 inches of space around each donut. Allow to rise until slightly risen, about 45 minutes to 1 hour.
While the donuts are rising, prepare the oil. In an 8- to 12-quart heavy stockpot, heat 2 quarts of neutral oil to 365°F. Safflower oil is a great choice for this.
When the donuts have risen, fry in batches, not more than four at a time, or the oil will cool down too quickly. Once lightly browned, turn the donuts over to fry the opposite side, about 1-2 minutes per side. When evenly browned, remove donuts from the oil and place them on a cooling rack.
Bring the oil back to 365°F and continue to fry until all donuts and holes are finished.
Once everything is fried, prepare the glazes.
When the donuts have cooled, dip them in the preferred glaze.
For the vanilla glaze
In a bowl, combine the powdered sugar, milk, and vanilla extract and whisk until smooth. For a thicker glaze, add more sugar. For a thinner glaze, add more milk.