Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, granulated sugar, and salt in a medium bowl. Cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal. Press flour mixture evenly into bottom of an 8-inch square baking pan coated with cooking spray, using a piece of plastic wrap to press mixture firmly into pan. Remove plastic wrap. Bake at 350° for 20 minutes or until lightly browned.
Combine brown sugar and corn syrup in a medium saucepan; bring to a boil over medium heat, stirring gently.
Combine egg and egg whites in a medium bowl. Stir one-fourth warm syrup mixture into eggs; add to remaining warm syrup mixture. Stir in pecans and vanilla. Pour mixture over crust.
Bake at 350° for 30 minutes or until set (the filling will puff up as it bakes but will deflate as it becomes set). Remove from oven; cool completely in pan on a wire rack. Cut into squares.