Preheat oven to 350°.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 4 ingredients (flour through salt) in a medium bowl. Combine the brown sugar, oil, molasses, and egg whites in a large bowl, stirring well with a whisk. Add flour mixture; stir until well-blended. Stir in walnuts. Drop by level tablespoons 2 inches apart onto baking sheets coated with cooking spray. Bake at 350° for 10 minutes. Cool 3 minutes on pans. Remove from pans; cool on wire racks.