PreparationMake cookies: Put oven racks in upper and lower thirds of oven and preheat oven to 350°F. Butter 2 large baking sheets. Whisk together flour, baking soda, and salt in a bowl. Stir together buttermilk and vanilla in a cup. Beat together butter and sugar in a large bowl with an electric mixer at medium-high until pale and fluffy, about 3 minutes, then add egg, beating until combined well. 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. Drop rounded teaspoons of batter 1 inch apart onto baking sheets. 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. Make peanut butter frosting: Mix peanut butter and butter together with a hand mixer. Gradually blend in the sugar and half and half. Blend until fluffy and light. Can be prepared a day or two in advance, tightly wrapped, and refrigerated. Allow to come to room temperature before using. Make chocolate frosting: Mix cocoa and butter together with a hand mixer. Gradually blend in the sugar and half and half. Blend until fluffy and light. Can be prepared a day or two in advance, tightly wrapped, and refrigerated. Allow to come to room temperature before using. Frost cookies: With offset spatula, spread peanut butter frosting over half of flat side of each cookie. Starting with cookies you iced first, spread chocolate frosting over other half.
PreparationMake cookies: Put oven racks in upper and lower thirds of oven and preheat oven to 350°F. Butter 2 large baking sheets. Whisk together flour, baking soda, and salt in a bowl. Stir together buttermilk and vanilla in a cup. Beat together butter and sugar in a large bowl with an electric mixer at medium-high until pale and fluffy, about 3 minutes, then add egg, beating until combined well. 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. Drop rounded teaspoons of batter 1 inch apart onto baking sheets. 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. Make peanut butter frosting: Mix peanut butter and butter together with a hand mixer. Gradually blend in the sugar and half and half. Blend until fluffy and light. Can be prepared a day or two in advance, tightly wrapped, and refrigerated. Allow to come to room temperature before using. Make chocolate frosting: Mix cocoa and butter together with a hand mixer. Gradually blend in the sugar and half and half. Blend until fluffy and light. Can be prepared a day or two in advance, tightly wrapped, and refrigerated. Allow to come to room temperature before using. Frost cookies: With offset spatula, spread peanut butter frosting over half of flat side of each cookie. Starting with cookies you iced first, spread chocolate frosting over other half.