Beat first 4 ingredients at medium speed with an electric mixer until well blended. Add eggs, 1 at a time, beating until blended.
Combine flour, baking powder, and salt. Gradually add flour mixture to sugar mixture; beat until blended. Stir in almonds and vanilla.
Using floured hands, shape dough into a 10-inch log on a lightly greased baking sheet, and flatten to 1-inch thickness.
Bake at 350° for 30 minutes. Remove to a wire rack to cool completely. Reduce oven temperature to 300°.
Cut log diagonally into 1/2-inch-thick slices with a serrated knife, using a gentle sawing motion. Place slices on an ungreased baking sheet. Bake at 300° for 20 to 25 minutes (cookies will be slightly soft in center but will harden as they cool). Remove to wire racks to cool completely.