These cookies are designed for those who can't choose between chocolate and vanilla. Half of each cookie is coated with chocolate icing and the other half with vanilla.
Position an oven rack in center of oven and one in lower third. Heat oven to 350°F.
Combine flour, baking powder, soda and salt on waxed paper. Beat together butter and sugars in large bowl until creamy, about 2 minutes. Beat in buttermilk, egg and vanilla until well blended. On low speed, beat in flour mixture in 3 batches.
Drop batter by level 1/4 cup onto 2 large baking sheets, spacing about 3 inches apart. Using metal spatula, spread into 2-inch circles.
Bake in 350°F oven for 8 minutes; switch baking sheets. Bake another 7 to 9 minutes or until edges are lightly browned. Cool baking sheets on wire rack 1 minute. Transfer cookies to wire rack to cool completely.
For black or chocolate icing, melt chocolate chips and vegetable shortening in top of double boiler over hot, not boiling water, until smooth. Let cool. For white icing, beat milk, confectioners sugar and salt in bowl until spreading consistency, adding more milk if necessary; cover with plastic wrap.
When cookies are cooled, brush off crumbs. Spread half of flat side of each cookie with 1 tablespoon white icing. Let dry. Spread other half of flat side of each cookie with 2 teaspoons chocolate icing. Let dry. Store between sheets of waxed paper in sealed container.