Beat together eggs, egg yolks, and sugar until very light and fluffy (10 minutes by hand). Add cream, and flavorings.
Stir in 1 cup of flour which has been sifted with the baking powder. Add enough additional flour to make a stiff dough. (Probably around 2-1/2 cups, but you have to do it by feel.) DO NOT OVERWORK or they will be tough.
Roll out and cut. Fry in hot oil. Dust with powdered sugar.