Pour enough oil into a large pot to give you about an inch of oil. Heat the oil to 365°F, over medium-high heat. Use a frying thermometer or a candy thermometer to ensure proper temperature. While oil is heating, prepare donuts, keeping an eye on the oil temperature.
In a small bowl, mix ½ cup sugar, cinnamon, and nutmeg (for dipping finished donuts in). Set aside.
In a medium bowl, whisk together flour, 1/2 cup sugar, baking powder, salt, cinnamon, ginger, nutmeg, and cloves.
In a separate bowl, whisk together pumpkin, buttermilk, vanilla, and melted butter.
Add the buttermilk mixture to the flour mixture, and using a fork, mix just until combined. Do not over mix.
On a floured surface with a floured rolling pin, roll dough to ½-inch thickness. The dough is sticky, so be generous with the flour. Then, using a 2¾-inch pastry cutter and a 1-inch pastry cutter, cut out donuts and donut holes, placing cut donuts on a parchment paper-lined baking sheet or cutting board. Re-roll as needed to use all the dough.
Once your oil has reached 365°F, place no more than 3 donuts in the oil at a time (or you run the risk of cooling your oil too much). Fry for about 2 minutes, flipping once. Donuts are done when they are golden brown on both sides. Move to a paper towel-lined cooling rack to cool. **Keep an eye on your oil temperature and adjust the heat up or down to maintain a temperature of 355°F to 365°F.**
Allow fried donuts to cool for 1 minute before dipping them in sugar and spices, coating all sides.
Continue the process until all donuts are fried and coated with sugar.
Fry donut holes using the same method, frying no more than 10 at a time.