Preheat oven to 350°.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 8 ingredients (through basil) in a large bowl.
Combine milk, oil, eggs, and egg white; stir with a whisk. Add milk mixture to flour mixture, stirring until well blended. (Dough will be crumbly and slightly dry.)
Turn dough out onto a lightly floured surface; knead 7 times. Divide dough in half. Shape each portion into an 8-inch-long roll. Place rolls, 6 inches apart, on a baking sheet coated with cooking spray; flatten to 1-inch thickness. Bake at 350° for 25 minutes. Remove from baking sheet; cool 10 minutes on wire rack.
Reduce oven temperature to 325°.
Cut each roll diagonally into 12 (1/2-inch) slices; stand slices upright on baking sheet. Bake 25 minutes (cookies will be slightly soft in center but will harden as they cool). Remove from baking sheet; cool completely on wire rack.