Preheat oven to 350°.
Lightly spoon flours into dry measuring cups, and level with a knife. Combine flours and salt in a bowl; stir well with a whisk.
Beat sugar and eggs with a mixer at high speed until thick and pale (about 4 minutes). Add oil and extracts, beating until well-blended. Add flour mixture, beating at low speed just until blended. Stir in cherries and chocolate chips.
Divide dough in half; turn out onto a baking sheet coated with cooking spray. Shape each portion into a 10-inch-long roll, and flatten to 1-inch thickness. Bake at 350° for 25 minutes or until lightly browned. Remove rolls from the baking sheet; cool 10 minutes on a wire rack. Reduce oven temperature to 325°.
Cut each roll diagonally into 20 (1/2-inch) slices. Place slices, cut sides down, on baking sheet. Bake at 325° for 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; cool completely on wire rack.