Cream butter in a medium mixing bowl; gradually add sugar, beating until light and fluffy. Add milk, egg yolk, and vanilla, stirring well.
Sift together flour, baking powder, and salt; add to creamed mixture, stirring until well blended.
Divide dough in half; set one half aside. Add melted chocolate to remaining dough; stir until well blended. Chill.
Roll light half of dough to a 14- x 6-inch rectangle on waxed paper; set aside. Repeat procedure with chocolate dough. Gently place chocolate rectangle directly on top of light rectangle; remove waxed paper. Roll up jellyroll fashion, beginning at long side; wrap in waxed paper, and chill 1 hour.
Cut into 1/4-inch slices. Place 2 inches apart on greased cookie sheets. Bake at 375° for 8 to 10 minutes. Cool slightly on cookie sheets, and remove to wire racks.