Cream butter in a large mixing bowl; gradually add sugar, beating until light and fluffy. Add eggs, one at a time, beating well after each addition. Add melted chocolate and vanilla, beating until well blended.
Combine flour, baking powder, and salt; add to creamed mixture, stirring well. Stir in walnuts.
Divide dough in half; shape each half into a roll, 2 inches in diameter. Wrap in waxed paper, and chill overnight or until firm.
Cut dough into 1/8-inch slices; place 2 inches apart on ungreased cookie sheets. Bake at 350° for 8 to 10 minutes. Remove from cookie sheets, and cool on wire racks.