In the bowl of a stand mixer with the dough hook attachment, combine the warm milk, yeast, sugar, eggs, pumpkin puree, butter, and vanilla.

Slowly add the dry ingredients to the wet, mixing between additions. Once all of the dry ingredients are added, mix for an additional 4-5 minutes.

Transfer the dough into a medium sized bowl that has been greased. Cover with a clean kitchen towel or plastic wrap and let it rise for 1 hour or until it doubles.

Transfer the dough to a well-floured work surface and using a rolling pin roll the dough to about a 1/4-inch thickness. Using a donut cutter or a 3-inch circle cookie cutter, cut as many donuts as you can. Re-roll the leftover dough until you have none left. You should get 20 donuts.

Transfer the cut donuts to a baking sheet lined with parchment paper that has a light coating of all-purpose flour. Cover with a clean kitchen towel and let proof for 45-60 minutes or until doubled in size.

Pour oil in a large pot or deep fryer and heat the oil to 325°F. Fry the donuts for 1-2 minutes on each side or until golden. Using a slotted spoon or a spider strainer, transfer the fried donuts to a baking sheet lined with paper towels to help absorb excess oil.

In a small bowl combine the granulated sugar, cinnamon, and nutmeg. Coat each donut thoroughly, tossing the donuts in the sugar to coat every part of the donut.

Serve the donuts when they are warm and just came out of the fryer. Enjoy!