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1
Put oven racks in upper and lower thirds of oven and preheat oven to 350F.
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2
Butter 2 large baking sheets.
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3
Whisk together flour, baking soda, and salt in a bowl.
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4
Stir together buttermilk and vanilla in a cup.
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5
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.
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6
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.
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7
Drop rounded teaspoons of batter 1 inch apart onto baking sheets.
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8
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.
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9
Transfer to a rack to cool.
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10
Mix peanut butter and butter together with a hand mixer.
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11
Gradually blend in the sugar and half and half.
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12
Blend until fluffy and light.
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13
Can be prepared a day or two in advance, tightly wrapped, and refrigerated.
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14
Allow to come to room temperature before using.
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15
Mix cocoa and butter together with a hand mixer.
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16
Gradually blend in the sugar and half and half.
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17
Blend until fluffy and light.
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18
Can be prepared a day or two in advance, tightly wrapped, and refrigerated.
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19
Allow to come to room temperature before using.
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20
With offset spatula, spread peanut butter frosting over half of flat side of each cookie.
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21
Starting with cookies you iced first, spread chocolate frosting over other half.
