Preheat an oven to 350 degrees F. Butter 12 muffin-tin wells or line them with paper muffin cups.
In a medium bowl, whisk together flour, cocoa, baking powder, baking soda, and salt; reserve.
In a large bowl, using an electric mixer set on medium-high speed, beat together the butter and sugar until light and fluffy. Add the egg and vanilla and beat well. Beat in the flour mixture in 3 batches, alternately with buttermilk.
Spoon into the prepared muffin tins, filling each cup about 2/3 full. Bake until a toothpick inserted in the center of the cake comes out clean, 16 to 20 minutes. Remove from the oven, let cool in the pan for 5 minutes, then transfer to a rack and let cool to room temperature.
To make the icing, place the egg whites in a bowl. Using an electric mixer set on high speed, beat until soft peaks form. Add the confectioners' sugar, vanilla, and orange juice and continue to beat until thick and shiny. If too thick, add more orange juice. If too thin, add more confectioners' sugar.
Transfer 1/3 of the icing to a small bowl and color with black or dark brown food coloring. Spoon this dark icing into a pastry bag fitted with a tip, or pour it into a plastic squeeze bottle.
Now, ice the cupcakes and make the cobwebs: Spoon the white icing into the center of the cupcake and spread with a small spatula or butter knife. Starting at the center of a cupcake, pipe a spiral of the dark icing from the center to the outer edge. Then, drag a sharp knife point from the center of the spiral to the edge of the cupcake. Wipe the knife clean, move about a 1/2-inch to the left or right and drag the knife in the opposite direction from the outer edge to the middle of the cupcake. Continue in this way until you have worked your way around the cupcake and formed the cobweb. Repeat with the remaining cupcakes.