Old-Fashioned Buttermilk Doughnuts

In a bowl, sift together the cake flour, baking powder, salt and nutmeg.
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and sugar together until mixture resembles coarse wet sand (see Notes). Add the egg yolks and mix until thick and pale yellow in color, about 3-4 minutes.
Add the flour mixture to the bowl in 3 additions, alternating with the buttermilk, starting and ending with the dry ingredients, scraping the sides of the bowl down as necessary. The dough will be sticky.
Cover with plastic wrap and chill for 1 hour and up to 24 hours.
On a floured surface, roll out the chilled dough to about ½ inch thick. Use a doughnut cutter or two differently sized round cutters to cut out 3-4 inch doughnuts, dipping the cutters into flour as necessary to prevent sticking.
Pour the oil into a heavy bottomed pot to at least 2-4 inches deep. Insert a thermometer and heat to 350°F over medium-high heat.
Add the donuts to the heated oil a few at a time, careful not to overcrowd the pot. Fry on each side about 2 minutes until golden brown, and watch to make sure they don’t burn. Doughnut holes will fry about 1 minute on each side.
Remove with a slotted spoon and set on paper towels to drain.
Fry remaining doughnuts, adjusting heat as needed to maintain 350°F.

Mix all ingredients in a bowl with a whisk until smooth. Dip each donut into the glaze, flipping to cover both sides, making sure they are covered completely. Place on a wire rack above a sheet pan to catch any excess glaze. Let sit for 10-20 minutes until glaze is set.
Doughnuts are best the day they are made, but will keep in an air tight container at room temperature for a few days.