In the large bowl of an electric mixer, cream together the margarine and sugar. Beat in the egg, egg yolk, and vanilla. Add the flour, folding in by hand. Spread the dough into a greased and floured 9x13" baking pan. Set aside and prepare the frosting.
Beat the egg white until it is stiff. Fold in the brown sugar. Spread the frosting over the cookie dough. Top with chopped nuts.
Bake at 350F. for 30 minutes. Let the bars cool in the pan, cut into bars and serve.