Step 1: Preheat your oven to 350°F (175°C) and lightly grease two 6-cavity doughnut pans with non-stick spray or butter.
Step 2: In a large mixing bowl, whisk together the flour, granulated sugar, brown sugar, baking powder, pumpkin pie spice, salt, and baking soda until well combined.
Step 3: In a separate medium bowl, whisk the pumpkin puree, eggs, melted butter, and vanilla extract until smooth.
Step 4: Pour the wet ingredients into the dry ingredients and fold together using a rubber spatula just until no streaks of flour remain. Do not overmix.
Step 5: Transfer the batter to a piping bag or a large zip-top bag with the corner snipped off. Pipe the batter into the prepared doughnut pans, filling each cavity about 3/4 full.
Step 6: Bake for 10-12 minutes, or until a toothpick inserted into the center comes out clean and the tops spring back when touched.
Step 7: Allow the doughnuts to cool in the pan for 5 minutes, then carefully turn them out onto a wire cooling rack to cool completely.
Step 8: Once cooled, dip the tops into a simple glaze or a mixture of cinnamon and sugar before serving.