Cream butter in a medium mixing bowl; gradually add sugar and salt, beating until light and fluffy. Add egg, beating well.
Stir melted chocolate and vanilla into creamed mixture. Stir in flour. Chill 1 hour.
Roll to 1/4-inch thickness on a lightly floured surface. Cut with a 2-inch round cutter. Place 2 inches apart on lightly greased cookie sheets; bake at 425° for 6 to 8 minutes. Cool slightly on cookie sheets. Remove to wire racks to cool completely.