Beat the 4 egg whites in medium-sized bowl until stiff but not dry. Reserve.
Combine 2 egg yolks (discard the other 2 egg yolks), buttermilk, flour sugar, baking powder, baking soda, salt, cardamom, vanilla extract, and melted butter in a bowl, and mix until smooth. Fold in the beaten egg whites.
Pour about 3/4 teaspoon oil into each round of an aebleskiver pan and heat over medium-high heat on top of stove. Add a heaping tablespoon of batter, or enough to fill each round about three-quarters full. When bubbly around the edges, turn each round upside down with chopsticks or a fork. Continue cooking turning frequently, until the rounds are golden on all sides and done in middle, about 5 minutes. Remove each cake as it is done and drain on paper towels. Keep warm in an oven at 200 until all the rounds are cooked. Sprinkle with powdered sugar. Makes 4 pans.