For the doughnuts, whisk together the flour, baking powder, salt, nutmeg, and pumpkin pie spice in a medium bowl and set aside.

In the bowl of a stand mixer fitted with the paddle attachment, mix the sugar and shortening for 1 minute on medium speed. Add the egg yolks and mix for 1 minute; the mixture will be light yellow and thick.

Have your flour mixture, sour cream, and pumpkin ready. Add roughly 1/3 of the flour mixture and mix until combined. Add the sour cream and mix until combined. Add another 1/3 of the flour mixture and mix until combined. Add the pumpkin, mix until combined, then add the final 1/3 of the flour mixture and mix until just combined. The dough should be wet and sticky like cookie dough.

Transfer the dough to a clean bowl and cover with plastic wrap. Refrigerate for at least 45 minutes, but up to 24 hours.

Before frying the doughnuts, make the glaze. Whisk together all the ingredients except for the milk. Slowly add the hot milk, whisking constantly, until the mixture is smooth. Set aside. This step can also be done in the bowl of a stand mixer, but I found it just as easy to do it by hand.

Heat at least 2 inches of oil in a heavy duty pot or Dutch oven to 325 degrees (use a candy thermometer).

While the oil is heating, sprinkle some additional flour onto a work surface. See important notes below for details.

Place the dough on the floured work surface and flour your hands and a rolling pin. Roll the dough out to about 3/4" thickness and then flip it over and roll it down to 1/2". Dip a 2 1/2" biscuit or doughnut cutter into some flour and then cut the doughnuts. Re-roll and cut the scraps until either the dough becomes too springy or you run out of dough.

When the oil reaches 325, shake off excess flour from the cut dough pieces and carefully add them to the pot, a few at a time (depending on the size of your pot--just don't crowd the pot and you'll be fine). Once the doughnuts float to the surface, fry for about 15 seconds and then flip them. Fry for 75-90 seconds or until they're golden brown and cracked, then flip back to the first side and fry for another 60-75 seconds or until golden brown. Transfer to a paper towel-lined tray or plate and repeat with the remaining dough.

While the doughnuts are still hot, dip the side with the deepest cracks deeply into the pumpkin glaze. Allow to cool on a wire rack for 15 minutes before serving. Makes 12-15 doughnuts.