Our mother hen was baked in an ovenproof mixing bowl, and then carved into shape; the chocolate cake is covered in feathers of piped buttercream; she roosts atop a nest of spun sugar. For the decorating technique, see our step-by-step photos.
Preheat oven to 350 degrees. Butter an ovenproof 10-inch-diameter 5-quart bowl. Dust with flour, and tap out excess.
Sift cocoa, flour, sugar, baking soda, baking powder, and salt together into the bowl of an electric mixer. Add eggs, 2 cups warm water, buttermilk, oil, and vanilla. Beat mixture on low speed until smooth, about 3 minutes.
Transfer batter to prepared bowl. Bake until a tester comes out clean, about 1 hour and 45 minutes. Transfer to a wire rack; let cool in bowl 45 minutes. Unmold onto rack. Let cool completely.
Place cake, broad side up, on a cutting board. Using a long serrated knife, cut a crescent-shaped piece off both sides to create a football-shaped body; reserve scraps. Cut 1 of the scraps crosswise at an angle to create a tail that follows the upward slope of the bowl; set aside. Cut the other scrap crosswise at an angle to create a neck that is longer than the tail, and that curves up, following the upward slope of the bowl.
Attach tail and neck with white buttercream. Cut a small round piece from the remaining cake scraps to create the back of the head. Trim 1 side to be flat; attach flat side to back of neck. Refrigerate assembled cake until buttercream is firm, at least 20 minutes. Spread a thin layer of buttercream over cake. Refrigerate until firm, at least 20 minutes.
Transfer remaining white buttercream in batches to a pastry bag fitted with a small ridged tip. Pipe feathers, beginning at base of cake and working up, overlapping: Hold tip flat against side of cake (ridges facing out). Pipe enough for 1 feather (1/2 to 1 inch long), then abruptly release pressure on the bag to let buttercream come almost to a point. Cover body, including head. Using the #46 tip and the red-orange buttercream, pipe feathers in center of tail and on sides of body for wings.
Switch to an open-prong tip. Pipe 2 drooping U shapes side by side under where the beak should be, creating a teardrop-shaped wattle. Pipe overlapping shell curls on top of the head for the scalloped comb: Start at front of head and pipe forward a short line, then pipe up and back over it; start next line in middle of the one before. Transfer yellow-orange buttercream to a pastry bag fitted with just a coupler; pipe a beak. Using kitchen tweezers, place 2 licorice pieces above beak for eyes.
Refrigerate cake until buttercream is firm, at least 30 minutes or up to 2 days.