Cream shortening in a large mixing bowl; gradually add sugar, beating well. Add egg, beating well.
Combine flour, cocoa, soda, baking powder, and salt; mix well. Add to creamed mixture alternately with milk, beginning and ending with flour mixture; stir well. Stir in vanilla.
Drop mixture by teaspoonfuls onto ungreased cookie sheets. Bake at 375° for 8 minutes. Remove from cookie sheets, and cool completely on wire racks. Spread half of cookies with filling; top with remaining cookies.