In a large bowl, combine the flour, 1 cup sugar, baking powder, salt and baking soda. Cut in shortening until mixture resembles coarse crumbs.
In a small bowl, whisk the egg yolks, 2 egg whites, milk and vanilla; gradually add to crumb mixture, tossing with a fork until dough forms a ball. Divide in half, making one portion slightly larger.
Roll out larger portion of dough between two large sheets of waxed paper into a 17-in. x 12-in. rectangle. Transfer to an ungreased 15-in. x 10-in. x 1-in. baking pan. Press pastry onto the bottom and up the sides of pan; trim pastry even with top edges. Spread apricot filling over dough; sprinkle with walnuts.
Roll out remaining pastry to fit top of pan; place over filling. Trim, seal and flute edges. Cut slits in top. Whisk remaining egg white; brush over pastry. Sprinkle with remaining sugar.
Bake at 350° for 35-40 minutes or until golden brown. Cool on a wire rack.