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. 1/2 cup at a time, mix in the dry ingredients. Scrape the sides and mix until just combined. 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 a floured surface or silpat until it's a 1/2 inch thickness. Make sure not to over-knead the dough. Use a doughnut cutter or 2 concentric circle cutters to cut out all the doughnuts. *See note about sizing. Put the cut doughnuts back in the refridgerator.
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 over a bowl of warm water and occasionally stir to keep a hardened layer from forming while you fry the doughnuts.
Into a large, deep pan, add about 2 inches of oil and heat to 325 F. Set a wire rack over paper towels or a baking sheet. Two at a time, add the doughnuts so they do not touch. Fry on each side for 2 minutes until they are golden brown and transfer to the wire rack.
As soon as the doughnuts are cool enough to touch but still warm, dip them into the glaze and flip to cover the entire doughnut. Transfer back to the cooling rack for about 5 minutes until glaze is set and cooled. A slightly warm doughnut will have a more even glaze. If necessary, you can put the doughnuts in the microwave for 10-15 seconds to warm them up again.
Doughnuts are best eaten the same day but can be stored in an airtight container overnight.