For the doughnuts:
3½ cups all-purpose flour
4 teaspoons baking powder
½ teaspoon baking soda
1 teaspoon salt
2 teaspoons ground cinnamon
1 teaspoon ground ginger
½ teaspoon ground nutmeg
¼ teaspoon ground cloves
1 cup sugar
3 tablespoons unsalted butter, at room temperature
1 large egg
2 large egg yolks
1 teaspoon vanilla extract
½ cup buttermilk
1 cup canned pure pumpkin
Canola or peanut oil (for deep-frying)
For the cinnamon-sugar:
½ cup sugar
2 teaspoons cinnamon
For the spiced glaze:
1 cup powdered sugar
¼ teaspoon ground cinnamon
Dash of ground nutmeg
Dash of ground ginger
Dash of ground cloves
2 tablespoons milk
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg and cloves and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat together the sugar and butter until well blended. Add egg, then yolks and vanilla. Continue beating while gradually adding the buttermilk. Beat in the pumpkin about ¼ cup at a time. Gradually fold the flour mixture into the egg mixture, then cover and refrigerate for about three hours.
Line two baking sheets with parchment or wax paper and lightly flour your work surface. Gently roll dough to about ½-inch thickness.
Using a floured 2½-inch round cutter, cut out dough rounds. Use a floured 1-inch cutter to remove the centers (we used the bottom of a 1M piping tip). Arrange the doughnuts and holes on the prepared baking sheets. Gather dough scraps and continue cutting until all the dough is used.
Line a cooling rack or two baking sheets with several paper towels. Add enough oil to a skillet or Dutch oven to reach a depth of 1½ inches. Heat oil until the temperature reaches 365º to 370º.
Fry doughnuts a few at a time, adjusting heat as needed to maintain temperature, until golden brown, about 1 minute per side. Fry doughnut holes in a couple batches, turning occasionally, until golden brown, about 2 minutes. Use a spider/strainer to transfer doughnuts to paper towels.
To make the cinnamon-sugar, whisk together the cinnamon and sugar in a small, shallow bowl until combined.
Make the spiced glaze by combining powdered sugar and spices in a small bowl. Add the milk and whisk to combine, until a thick glaze is formed. Add more milk as needed to achieve desired consistency.
When the doughnuts are just cool enough to handle, dip half in the cinnamon-sugar, turning to coat completely. Shake off excess. Dip the remaining doughnuts in the glaze and allow to set before serving.