In a bowl, whisk the cake flour, baking powder, salt, and nutmeg.
In a large bowl or stand mixer, cream the butter and sugar together. Add the egg yolks and sour cream and combine.
Pour the wet ingredients into the dry ingredients. With a spoon or spatula (do not use an electric mixer), stir by hand. The dough should be flakey but not overly dry or wet.
Wrap the dough in plastic wrap, spray the top of the dough with non-stick spray and put in the refrigerator for 1 hour.
Remove the plastic wrap and roll the dough out on floured parchment paper until it's ½-inch thickness. Make sure not to over-knead the dough. Use a donut cutter or 2 concentric circle cutters to cut out all the donuts. Reroll the dough as needed to get about 6-8 donuts and holes. Put the donuts back in the refrigerator while heating the oil.
Make the glaze. In a medium saucepan over low heat, add the milk and vanilla extract. Gradually add the powdered sugar and whisk until smooth. Remove from heat. Put the saucepan in some warm water and occasionally stir to keep a hardened layer from forming while you fry the donuts.
Into a large, deep pan, add about 2 inches of oil and heat to 325 F. Two or three at a time, add the donuts so they do not touch. Fry on each side for 2 minutes until they are golden brown and transfer to a wire rack over paper towels or a baking sheet. Donut holes only need about 45 seconds per side.
The oil temperature will decrease when you add the donuts. Let it come back up to 325 degrees between batches.
As soon as the donuts are cool enough to touch but still warm, dip them into the glaze and flip to cover the entire donut. Transfer to the cooling rack for about 5 minutes until glaze is set and cooled. If necessary, you can put the donuts in the microwave for 10-15 seconds to warm them up again.
Donuts are best eaten the same day but can be stored in an airtight container at room temperature for a few days.