Preheat your oven to 350°F. In a small bowl combine the flour, baking powder, cinnamon, cardamom and salt. In a bowl of a stand mixer (or large bowl) mix the butter and sugar together.
Add the egg and vanilla. Next add half of the flour mixture and mix.
Place the batter in a ziplock bag. Cut one of the corners on the ziplock bag and fill the donut pan ¾ full. Bake for 10-15 minutes.
For the topping, combine the sugar and cinnamon on a small plate. Allow the donuts to cool. Brush each of the donuts with melted butter. Place the donut in the sugar mixture and cover completely.