Preheat your oven to 375°F and position a rack in the middle. Grease a standard-sized doughnut pan or several mini doughnut pans with non-stick baking spray.
In a mixing bowl, combine the flour, brown sugar, espresso powder, spices, and salt using a whisk.
In another bowl, whisk together the pumpkin puree, sour cream, egg, and vanilla extract.
Combine the wet mixture with the dry ingredients, stirring gently with a spatula until just mixed. The batter will be thick.
Transfer the batter to a piping bag or a plastic bag and snip off one corner. Pipe the batter into the doughnut molds, filling them halfway.
Bake for about 11-12 minutes for standard-sized doughnuts or 8-10 minutes for mini doughnuts, until a toothpick inserted comes out clean.
Let the doughnuts cool in the pan for 1 minute, then turn them out onto a wire rack.
While they’re still hot, dip the doughnuts in the cinnamon and sugar mixture for a full coating. If the mixture doesn't stick well, lightly brush the doughnuts with melted or softened butter before coating.
Allow the doughnuts to cool on a wire rack for 10 minutes, then enjoy them warm!