Combine eggs, egg white, and vanilla; add to flour mixture, stirring until well blended (dough will be dry). Turn dough out onto a lightly floured surface; knead 7 or 8 times. Shape dough into a 16-inch long roll.
Place roll on a cookie sheet. which has been coated with cooking spray, and flatten roll to 1-inch thickness. Bake at 350°F for 30 minutes. Remove roll from cookie sheet to a wire rack; cool 10 minutes.
Cut roll diagonally into 24 (1/2-inch) slices. Place slices, cut sides down, on cookie sheets. Reduce oven temperature to 325°F; bake 10 minutes. Turn cookies over, and bake 10 additional minutes. (Cookies will be slightly soft in center but will harden as they cool). Remove from cookie sheets and cool completely on wire racks.