Cream shortening and sugar until fluffy; beat in egg, milk and chocolate.
Sift together flour, salt and baking powder. Stir into creamed mixture. Shape dough in two smooth rolls about 2" in diameter, 6" long. Wrap each in waxed paper and chill several hours until firm, or overnight.
Slice rolls thin, about ⅛", with sharp knife. Place 1½" apart on lightly greased baking sheet. Bake in moderate oven (375°) 7 to 10 minutes (watch carefully). Remove cookies and cool on racks. Spread half the cookies with Peppermint Frosting. Top with remaining cookies.