Heat the milk to 90° F. Add the yeast and a teaspoon of sugar and stir to combine. Set the mixture aside. Let sit for 10 minutes or until foamy.
½ cup milk, 2 tbsp dry active yeast, ¼ cup +1 tsp granulated sugar
Pour the milk mixture into the bowl of a stand mixer. Add the remaining sugar, eggs, butter, salt, nutmeg, and the flour. Lock the bowl into the mixer fitted with a dough hook and mix on low until a dough begins to form. This should take about 10 minutes.
¼ cup +1 tsp granulated sugar, 2½ cups all-purpose flour, 2 large eggs, 2 tbsp unsalted butter, 1½ tsp kosher salt, ½ tsp nutmeg
Transfer the dough to a floured surface and knead until smooth and elastic. This should take about 5-7 minutes. Form the dough into a ball and transfer it to a lightly oiled bowl. Cover and let rise for an hour and a half or until doubled in size. **
Once the dough has risen, transfer it to a well-floured surface and roll it out to a 1/4 inch thickness. Cut 12-14 donuts out of the dough using a 2 1/2 - 3 inch biscuit cutter. *** Transfer the cut donuts to a large baking sheet dusted with flour. Cover with a tea towel and let rise for 1 hour. The donuts will puff up slightly.
When your donuts have risen, heat 3 1/2 inches of oil in a large cast-iron skillet to 375° F. Add 4-5 donuts to the oil at a time depending on the size of your pan. Fry the donuts until golden on each side. About a minute on each side.
Transfer the fried donuts to a plate lined with a paper towel. Set them aside to drain and cool for about 30 minutes.