Beat the eggs until light. Add gradually the sifted sugar. Beat at least 3 to 5 minutes on medium speed with an electric beater, longer if beating by hand, then add the vanilla. Set aside.
Sift the flour before measuring. Resift with the baking powder and add the crushed anise seed. Add flour ingredients to egg mixture and beat the batter another 5 minutes.
Drop 1/2 teaspoon at a time, well apart, on a cookie sheet lined with foil. The dough should flatten to a 1-inch round but should not spread more. If it does, add a little more flour. Let the drops dry at room temperature 18 hours.
Bake the cakes until they begin to color, about 12 minutes. When done, they will have a puffed meringue-like top on a soft cookie base.