In a bowl, with an electric mixer on medium speed, beat butter and sugar until smooth. Beat in egg yolk until well blended. Stir or beat in flour until mixture is no longer crumbly.
Press dough evenly into a buttered and floured 10- by 15-inch baking pan. In a bowl, with a fork, beat egg white to blend. Brush evenly over dough with a pastry brush. Sprinkle pecans evenly over dough, then press them in.
Bake in a 275° oven until golden brown, about 45 minutes. While hot, cut into 1 1/2-inch squares. Let cool completely in pan.