First, make the dough. Whisk the flour, baking powder, baking soda, 1 1/2 teaspoons of the pumpkin pie spice, and the cinnamon together in a bowl to aerate them and set it aside. Then get out a stand mixer and combine the brown sugar, butter, pumpkin butter, and pumpkin puree in its bowl. Beat it all together until fluffy with the paddle attachment. Then slowly add in the milk and each egg one at a time. Finally, turn the speed to low and slowly add in the dry ingredients until you have a soft, sticky dough. Line a sheet tray with a silicone mat and turn the dough out onto it. Flour the top of it with a generous sprinkle and also flour your hands. Use your hands to gently spread the dough out to be about 1/2 inch thick and pretty much fill the sheet tray. Set it in the freezer for an hour. This makes it much easier to cut out and handle. 

When the hour is up, line another sheet tray with a silicone mat and get out a donut cutter. Cut out the donuts and the lovely holes that come with them, cutting them as close together as possible to yield as many as you can. You should get about 20 donuts and 20 holes. Line them all up on the sheet trays and return them to the freezer for another 30 minutes to firm up again. While that happens, get out a large skillet with deep sides and fill it with about 3 inches of canola oil. Heat it over medium high heat and use a deep fry thermometer to make sure the oil reaches and stays around 350 degrees. Fry the donuts in batches for about a minute on each side, removing them to a plate lined with paper towel to drain. While they cook, stir the remaining pumpkin pie spice and granulated sugar together. When the donuts are all fried, coat them all in the sugar and pumpkin pie spice. Serve immediately warm! They also keep well for a couple of days sealed in a container.