Instructions

1. Make the dough:
2. Sift 5 cups of the all-purpose flour with 7 teaspoons baking powder into a large bowl. Place 3 large eggs in a small bowl and whisk until well-beaten. Microwave 1 1/2 tablespoons unsalted butter in a small bowl until melted, about 30 seconds.
3. Place the eggs, melted butter, 2 cups granulated sugar, and 1 1/2 cups slightly warm mashed potatoes in the bowl of a stand mixer fitted with a paddle attachment. Beat on medium speed until smooth and well-combined. Add 1 cup whole milk, 1 teaspoon kosher salt, 1 teaspoon ground nutmeg and mix to combine. Add the flour mixture and mix on low speed until just combined. Cover the bowl with plastic wrap and refrigerate overnight.
4. Heat 1 1/2 quarts vegetable oil in a 5-quart Dutch oven over medium-high heat until 375ºF. Meanwhile, prepare the coatings and glaze.
5. Make the coatings:
6. Place 1 cup granulated sugar and 2 tablespoons pumpkin spice in a small bowl and whisk until combined.
7. Place 2 cups powdered sugar in a small bowl and have a small fine strainer ready.
8. Make the vanilla glaze:
9. Place 1 cup powdered sugar, 2 tablespoons whole milk, and 1 teaspoon vanilla extract in a small bowl and whisk to combine.
10. Fry the doughnuts:
11. Sprinkle 1/3 cup of the all-purpose onto a clean work surface. Transfer 1/3 of the dough onto the floured surface; keep the remaining dough refrigerated. Using lightly floured hands, knead the dough a couple of times into some of the flour until stiff enough to handle. Pat to about 1/2-inch thick. Cut doughnuts out with a floured doughnut cutter (or use 2 round cutters about 3 and 1-inch in diameter). If the dough is too soft to cut out, work in some more of the flour from the surface. Separate the doughnuts and doughnut holes and discard any dough scraps.
12. Use a thin metal spatula coated in flour to carefully transfer half of the formed doughnuts into the hot oil. Fry, flipping once, until golden-brown and cooked through, about 2 minutes per side. Transfer to a paper towel-lined baking sheet to drain briefly. Dip the tops in the vanilla glaze, then set on a wire rack glazed-side up. Repeat frying and glazing the remaining formed doughnuts. Fry the doughnut holes until golden and cooked through, about 90 seconds per side. Drain, roll in the glaze, and place on the wire rack.
13. Repeat shaping, frying, and rolling the second portion of dough, then roll these doughnuts in the pumpkin spice sugar coating. Repeat shaping, frying, and rolling the final portion of dough, then roll these doughnuts in the powdered sugar.