Heat oven to 350°F. Coat 2 baking sheets with cooking spray. In medium-size bowl, combine flour, baking soda and salt. In large bowl with electric mixer on medium speed, 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, ending with flour mixture; beat until smooth.
Onto prepared sheets, for each cookie, drop 1/4 cup dough, spacing about 3 inches apart.
Bake 1 sheet at a time in 350°F oven 13 minutes, until wooden pick inserted in centers tests clean. Remove cookies to rack to cool.
In medium-size bowl, stir together confectioners sugar, corn syrup, vanilla and 2 tablespoons plus 1 to 2 teaspoons milk until smooth but thick enough to coat cookie. Remove 1/4 cup icing to small bowl; stir in cocoa powder and remaining 2 teaspoons milk until smooth.
Turn cookies flat side up. Spread white icing over one half of flat side of each cookie, and chocolate icing over other half. Let stand at room temperature until set. Store airtight at room temperature for up to 3 days.