Cookies. Heat oven to 350 degrees F. Cover 2 baking sheets with nonstick aluminum foil; set aside.
In medium-size bowl, combine flour, baking soda and salt. In large bowl, beat together sugar and butter until smooth and creamy, about 1 minute. Beat in egg until well combined. On low speed, alternately beat in flour mixture and the buttermilk, beginning and ending with flour mixture.
Drop 1/4 cupfuls of dough onto prepared baking sheets, spacing 3 inches apart and spreading into large circles, about 4 inches across.
Bake at 350 degrees F for 13 minutes or until toothpick inserted in centers tests clean. Remove cookies to rack to cool.
In medium-size bowl, stir together confectioners' sugar, 3 tablespoons milk and vanilla until smooth but thick enough to coat cookie. Set aside 1/2 cup icing in small bowl; stir cocoa powder and remaining 2 teaspoons milk into bowl until smooth.
Turn over cookies. Spread white icing over one half of each cookie, and chocolate icing over other half. Let stand at room temp until set, about 1 hour.