Combine first 5 ingredients in a large bowl. Combine vanilla and next 2 ingredients; add to flour mixture, stirring until well-blended (dough will be dry).
Turn the dough out onto a lightly floured surface, and knead lightly 7 or 8 times. Shape dough into a 16-inch-long roll. Place roll on a baking sheet coated with cooking spray, and flatten roll to 1-inch thickness.
Bake at 350° for 30 minutes. Remove roll from baking sheet to a wire rack, and let cool 10 minutes. Cut roll diagonally into 24 (1/2-inch) slices, and place, cut sides down, on baking sheet. Reduce oven temperature to 325°, and bake 10 minutes. Turn cookies over, and bake an additional 10 minutes (cookies will be slightly soft in center but will harden as they cool). Remove from baking sheet; let cool completely on wire rack.