Preheat oven to 350 degrees (F). Generously grease a doughnut pan; set aside.
In a large bowl whisk together the dry ingredients. In a separate bowl whisk together the pumpkin puree, melted butter, and egg. Gently fold the wet mixture into the dry mixture - don't over mix!
Spoon or pipe mixture into prepared doughnut pan, and bake for 10-11 minutes, or until the doughnuts spring back when lightly pressed. Allow doughnuts to cool a few minutes in the pan before transferring to a wire wrack to cool for a few more minutes.
For the glaze:
In a wide, shallow bowl combine the confectioners' sugar, pumpkin spice, milk, and vanilla. Whisk well to combine. If the glaze is too thick, add more milk, a half teaspoon at a time; if the mixture is too thin add more confectioners' sugar, two tablespoons at a time. Once you reached your desired consistency, dunk donuts in the glaze, using a fork to turn the donut over in the glaze so both sides are coated. Repeat with all donuts.
These donuts are best eaten the day they are made.
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