Microwave the milk for 30 seconds. Pour it into the bowl of a stand mixer. Stir in the yeast and sugar and let proof for 5 minutes.
Add the egg, shortening, pumpkin, spices, vanilla and coffee and stir to combine.
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Add the flour and salt and knead with a dough hook on medium speed until it pulls away from the sides and forms a ball.
Place the dough ball on the counter and cover with the mixing bowl. Let rise for an hour.
Remove the bowl. Gently roll the dough out on a lightly floured surface until it’s about one-inch thick.
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Using a 3-inch circle cookie cutter, cut out 8 circles. You will need to knead together scrap pieces of the dough to form the last few circles.
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Use a one-inch circle cookie cutter to cut out the centers. Save those for doughnut holes.
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Cover the doughnuts and doughnut holes gently with plastic wrap and let rise for 30 minutes.
Heat the vegetable oil in a large pot until it reaches 350 degrees F (175C).
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Slide 3 doughnuts into the hot oil and let fry for 1-2 minutes.
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Flip using a fork or chopstick. Continue cooking until golden brown. Remove from the oil and drain on a rack-lined baking sheet. Continue cooking the doughnuts and doughnut holes.
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Combine all the glaze ingredients in a small bowl. Whisk until smooth.
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Dip the cooked doughnuts and holes in the glaze. Serve warm.
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Yield 8 doughnuts with 8 doughnut holes
or about 80 doughnut holes.
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