1. Heat oven to 180ºC . Spread almonds in single layer on baking sheet.
Bake, stirring occasionally, until lightly toasted, about 10 minutes. Remove from oven; cool, then chop coarsely.
2. Beat butter in large bowl of electric mixer on medium-high speed until very light and fluffy, 5 minutes. Add 3 tablespoons of the confectioners' sugar; continue beating 3 minutes.
3. Add egg yolks, Cognac and vanilla; beat until smooth. Beat in almonds, flour and baking powder until mixed well. (If dough is too soft to handle, add additional flour.)
4. Shape scant tablespoons full of dough between palms into round balls or crescents. Bake on ungreased baking sheets until set and very pale golden in color; 15 minutes. Remove cookies to cooling rack.
5. Place remaining confectioners' sugar into sifter. While cookies are still hot, sift confectioners' sugar over tops. Repeat twice at 20-minutes intervals.