Beat the 2 egg whites in a medium-sized bowl until stiff but not dry. Reserve.
Combine 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 the batter, or enough to fill each round about three-quarters full. When bubbly around the edges, turn each round upside down with a long pick. Continue cooking, turning frequently, until done, about 5 minutes. Sprinkle with powdered sugar.
Aebleskiver pans can be purchased from our gift hutch. These pans sell for $13.95 plus tax, shipping and handling charges. We ship all over the country. Call or e-mail your order and we will take care of the rest!