Beat eggs in a medium mixing bowl until thick and tripled in volume; gradually add sugar, beating well. Stir in flour, baking powder, salt, and vanilla. Stir in walnuts.
Drop dough by teaspoonfuls 2 inches apart onto parchment or aluminum foil-lined cookie sheets. Bake at 375° for 6 minutes or until lightly browned. Cool completely on cookie sheets, and store in airtight containers.