How to Make It
Preheat the oven to 350° and line a 12-cup muffin pan with paper liners. In a bowl, whisk the flour with the cocoa powder, baking powder, salt and baking soda. In a large bowl, using a handheld electric mixer, beat the butter with the sugar at medium-high speed until fluffy. Beat in the eggs 1 at a time, then beat in the sour cream and vanilla until smooth. At low speed, beat in the dry ingredients. Scoop the batter into the lined muffin cups.
Bake the cupcakes in the center of the oven for about 17 minutes, until springy and a toothpick inserted in the centers comes out clean. Let cool slightly in the pan, then transfer to a rack to cool completely.
In a large bowl, using a handheld electric mixer, beat the butter at medium speed until smooth. Add the confectioners’ sugar, vanilla, salt and 2 tablespoons of the milk and beat at low speed just until combined, then beat at medium speed until smooth. Scrape half of the vanilla frosting into a medium bowl. Add the cocoa powder and the remaining 2 tablespoons of milk to the frosting in the large bowl and beat at low speed until fully incorporated.
Lay a large sheet of plastic wrap on a work surface with the long side facing you. Using a small spatula, spread the vanilla frosting in a 3-inch-wide strip down the center of the plastic wrap. Spread the chocolate frosting in a 3-inch-wide strip alongside the vanilla. Using the plastic, fold the chocolate frosting over the vanilla, twisting one end of the plastic to seal. Pull the twisted end of the plastic through a pastry bag fitted with a large star tip and cut off the protruding plastic at the tip. Refrigerate the frosting until barely firm, about 15 minutes. Pipe onto the cupcakes and serve.