Ingredients:
Cookies:
1 1/4 cups all-purpose flour
1/2 teaspoon baking soda
1/2 teaspoon salt
1/3 cup well-shaken buttermilk
1/2 teaspoon vanilla
7 tablespoons unsalted butter, softened
1/2 cup granulated sugar
1 large egg

Icings:
2 3/4 cups confectioners sugar
2 tablespoons light corn syrup
2 teaspoons fresh lemon juice
1/2 teaspoon vanilla
4 to 6 tablespoons water
1/4 cup unsweetened cocoa powder

Directions:

1. Preheat oven to 350°F.  Line 2 large baking sheets with parchment paper.
2. Prepare cookies:  Whisk together flour, baking soda, and salt in a bowl.
3. Stir together buttermilk and vanilla in a small bowl.
4. In a large bowl beat together the butter and sugar with an electric mixer at until pale and fluffy.
5. Add  the egg, beating until well combined. Reduce speed to low and add flour mixture and buttermilk mixture alternately in batches, beginning and ending with flour mixture, and mixing just until smooth.
6. Drop rounded tablespoons of batter 1 inch apart onto baking sheets OR fill a piping bag with the mixture and drop even rounds ( 2 inch diameter) onto baking sheets.
7. Bake, switching position of sheets halfway through baking, until tops are puffed, edges are pale golden, and cookies spring back when touched, 6 to 8 minutes total. Transfer to a rack to cool.
8. Prepare icing while cookies are cooling:  Stir together confectioners sugar, corn syrup, lemon juice, vanilla, and 2 tablespoons water in a small bowl until smooth. If icing is not of spreading consistency, add more water, 1/2 teaspoon at a time.
9. Transfer half of icing to another bowl and whisk in the cocoa, adding more water, 1/2 teaspoon at a time, to thin to same consistency as vanilla icing. Cover surface with a dampened paper towel, then cover bowl with plastic wrap.
10. Frost cookies:
    With offset spatula, spread white icing over half of flat side of each cookie.
    Starting with cookies you iced first, spread chocolate icing over other half.