Preheat the oven to 350℉. Lightly grease two standard doughnut pans or a 12-cup muffin pan.
In a large bowl, whisk together the oil, eggs, sugar, pumpkin puree, vanilla, pumpkin pie spice, salt, and baking powder until smooth. Add the flour, stirring just until smooth. Fill the wells of the doughnut pan or muffin pan about ¾ full, about a scant ¼ cup of batter in each well. I like to put the batter in my large pastry bag to evenly and easily fill the wells. (The recipe makes 15, so you will need to bake in two batches if you only have one doughnut pan.)
Bake the doughnuts for 15-18 minutes or until a cake tester inserted in one comes out clean. If you are making muffins, bake for 23-25 minutes. If you are making mini muffins, increase the temperature to 425℉ and bake for 7-8 minutes.
Meanwhile, in a shallow bowl whisk together the sugar and cinnamon; set aside.
Remove the doughnuts from the oven and let them cool for 5 minutes in the pan. Loosen the edges and gently coat them in the cinnamon sugar. If you have made muffins, sprinkle the tops heavily with the cinnamon sugar. Serve warm. Leftovers can be kept in an airtight container at room temperature for several days. Enjoy!