In a large bowl, cream butter and sugar until light and fluffy. Beat in egg yolks and vanilla. Combine the flour, baking powder, baking soda and salt; gradually add to the creamed mixture and mix well (mixture will be crumbly). Press into a greased 15x10x1-in. baking pan. Carefully spread with apricot preserves.
In a small bowl, beat egg whites until stiff peaks form. Carefully spread over preserves (egg white layer will be thin). Sprinkle with walnuts.
Bake at 350° for 25-30 minutes or until golden brown and edges are bubbly. Cool on a wire rack. Cut into squares. Refrigerate leftovers.