Preheat oven to 350°.
Lightly spoon flour into a dry measuring cup, and level with a knife. Combine flour and next 5 ingredients (flour through baking powder), stirring with a whisk. Set aside.
Combine oil, vanilla, and egg whites, and add to the flour mixture, stirring just until blended. Lightly coat hands with cooking spray.
Press the batter evenly into an 8-inch square baking pan coated with cooking spray. Bake at 350° for 18 minutes or until a wooden pick inserted in the center comes out clean. Cool in pan on a wire rack. Sift powdered sugar over top.