In a large bowl, sift together cake flour, baking powder, salt and nutmeg.
In the bowl of an electric mixer, beat together the butter and sugar until combined (it will have a texture similar to wet sand). Add the egg yolks and vanilla extract and beat until completely combined.
Gradually add about ⅓ of the flour mixture. Then add half of the sour cream. Add another ⅓ of the flour mixture, and then the rest of the sour cream. Finish with the remaining ⅓ of the flour mixture, beating just until the dough comes together. It will be sticky. Cover with plastic wrap and chill for 30 minutes in the refrigerator.
Line a large rimmed baking sheet with parchment paper. Set aside.
Roll the chilled dough onto a floured surface until it’s about ½-inch thick. Use a donut cutter or two round cutters (about 3-inches and 1-inch, respectively) to cut out the donuts and the donut holes. It’s helpful to dip the cutters in flour in between cutting each donut so that they don’t stick to the dough. Place on the parchment lined baking sheet. Cover with plastic and chill for about 30 more minutes.
Add enough oil to a pot so that the oil is at least 2 inches deep. Attach a deep-fry thermometer to the side of the pot. Heat the oil over medium heat until it reaches 340 degrees F.
When the oil has come to temperature, carefully place a couple of donuts into the pot. I usually cook the donuts in batches of 2-3 so that I don’t overcrowd the pot (which will bring down the temperature of the oil). As soon as a donut floats to the top, fry it for 40 seconds. It’s helpful to use a stopwatch at first (until you get the hang of the timing). After 40 seconds, flip the donut over and fry for 60-80 seconds on the other side (until the bottom is a nice golden brown color). Flip the donut one more time and cook for about 60-80 more seconds, until the other side is golden brown. Then remove the donut to a paper-towel lined tray.
Allow the donuts to cool for about 15 minutes before glazing.