Preheat the oven to 350 degrees. Spray 2 mini muffin tins with cooking spray and set aside.
In a medium bowl combine the flour, baking powder, salt, pumpkin pie spice, cinnamon, nutmeg, and cardamom.
In a large bowl cream together the pumpkin puree, brown sugar, and butter. Mix well.
Stir in the vanilla and egg and well combined.
Add the milk and mix until smooth.
Add the dry ingredients to the wet ingredients and stir until just combined.
Scoop the batter into as many muffin cups as possible filling each abotu 2/3 of the way full. I used one whole mini muffin tin and half of a second one.
Bake for 10-12 minutes or until a toothpick inserted into the center comes out clean.
Remove the donut holes to a wire rack and cool just enough so they are easy to handle.
Put melted butter in one bowl and combine the sugar, pumpkin pie spice, and cinnamon in another bowl.
Dip the donut holes first into the butter and then roll in the sugar mixture.
Serve warm.