Light, airy doughnuts with a surprise ingredient.
First, start by scalding the milk. Place in a small saucepan over medium high heat and watch closely until milk starts to steam and small bubbles form around the edge of the milk in the pan. Take pan off the heat and mix in shortening and sugar and allow milk to cool until it is slightly warmer than room temperature. The shortening should melt completely.
While milk is cooling, mix together the yeast and the water and allow yeast to dissolve. Lightly whisk eggs in a separate bowl.
Mix nutmeg, cinnamon, salt, and flour in the bowl of a stand mixer. In the mixer with the dough hook attached and the mixer running on low speed, add the milk, sugar, and shortening mixture to the dry ingredients. Add mashed potatoes, eggs and yeast mixture and let dough mix for several minutes, scraping down the sides and bottom to make sure the flour is getting incorporated. Let dough knead for about five minutes until the dough starts to look puffy in the bottom of the mixing bowl.
Remove dough and place in a lightly greased bowl and cover with plastic wrap. Proof until dough doubles in size, about one hour. After it has doubled, punch the dough down by grabbing the dough from the sides of the bowl and folding it over the middle, going around the width of the bowl so air has been removed. Allow to proof again until doubled in size, a little less than 30 minutes.
After the dough has completed its second rise, remove and place on a floured work surface. Roll out to about a 15" circle, the dough should be 1/4" inch thick. Cut out doughnuts with a 3.5" doughnut cutter. Place doughnuts and doughnut holes on a baking sheet lined with lightly-floured parchment paper. After the first doughnuts are cut out, you can rework the dough to roll out a few more. You should have about 16 doughnuts and holes. Allow doughnuts to proof until doubled in size again, about another 30 minutes.
In a large, heavy bottomed pot (such as a dutch oven) heat about 2" of oil until it reaches 360 F. At the same time, place a cooling rack over a rimmed baking sheet and place nearby. Mix ingredients for the glaze together in a large bowl.
Put about 3-4 doughnuts in the pot with the bottom of the doughnut touching the oil first. Fry each side for about 30 seconds, or until they are a medium brown color, but not burnt. Remove doughnuts with a slotted spoon or spider, and allow to cool for a few moments on the cooling rack. While the doughnuts are still warm, dip both sides in the glaze and place back on the cooling rack to drip.
Eat as soon as possible and enjoy!