Preheat the oven to 375. Thoroughly grease a standard-sized doughnut pan with non-stick spray.
In a bowl, whisk together the pumpkin, sour cream, egg and vanilla.
Separately, whisk together the flour, brown sugar, spices, baking soda and salt.
Add the dry ingredients to the wet, and stir together with a spatula until no dry streaks of flour remain.
The batter will be thick. Spoon the batter into a piping bag or a plastic bag, and snip off the corner. Pipe the batter into the doughnut pan.
Bake the doughnuts on the center oven rack for about 11-12 minutes, until a toothpick comes out clean. Cool the doughnuts in the pan for 1 minute, then turn out onto a wire rack.
Immediately dip the hot doughnuts in the cinnamon/sugar mixture to thoroughly coat them. If you have trouble with the cinnamon/sugar not sticking to the doughnuts, then use a pastry brush to lightly brush a very small amount of melted or soft butter on the doughnuts, and then coat them in the cinnamon/sugar.
Place the doughnuts on a wire rack, and cool for 10 minutes, then serve warm.