Combine flour and 1/2 cup sugar in a large mixing bowl; cut in butter with a pastry blender until mixture resembles coarse meal. Press mixture evenly into a greased 13- x 9- x 2-inch baking pan. Bake at 325° for 20 minutes or until set.
Beat egg yolks in a medium mixing bowl. Stir in remaining ingredients, except egg whites.
Beat egg whites (at room temperature) until stiff peaks form. Fold into coconut mixture. Spread mixture evenly over baked crust. Bake at 400° for 10 minutes; reduce heat to 350°, and bake an additional 20 minutes. Cool and cut into 1 1/2-inch squares.