Preheat oven to 350 degrees. Spray a nonstick donut pan with oil and set aside. Whisk together flour, baking powder, cinnamon, clove, ginger, nutmeg, and sea salt in a large bowl.
In another bowl, combine pumpkin puree, brown sugar, butter, eggs, and vanilla extract and mix until smooth. Add wet mixture to dry mixture and stir until just combined and you have a uniform batter with no dry pockets.
Transfer batter into a pastry bag or ziploc bag with one corner snipped off and pipe into prepared donut pan.
Place pan onto middle oven rack and bake for about 12 minutes or until tops of donuts are very slightly browned and a toothpick inserted in the center donut comes out clean. Place donuts onto cooling rack and allow to cool to room temperature.
Cream Cheese Frosting
Add all frosting ingredients to a bowl and beat with a hand or stand mixer until and smooth. Frosting should be thick but spreadable.
Place one donut, upside down, into bowl of frosting and gently press until halfway submerged. Twist the donut horizontally then lift it straight up out of the bowl. Repeat with remaining donuts until all are frosted.