1. Preheat oven to 325 degrees with rack in the center of the oven. Butter an 18-by-13-inch rimmed baking sheet, line with parchment paper, butter parchment, and set aside.

2. In a medium bowl, whisk together cocoa powder, food coloring, and 1/4 cup boiling water. Set aside to cool.

3. In the bowl of an electric mixer fitted with the paddle attachment, cream together butter and shortening on high speed until smooth. Add sugar and continue beating until light and fluffy, about 5 minutes. Add eggs, one at a time, beating well after each addition.

4. Stir buttermilk and vanilla into cocoa mixture. Into another medium bowl, sift together flour and salt. With the mixer on low, add flour mixture alternating with cocoa mixture, beginning and ending with flour mixture. Beat until incorporated.

5. In a small bowl, mix together vinegar and baking soda until baking soda dissolves; mixture will fizz. Add to batter and mix until just combined.

6. Pour batter into prepared baking sheet, smoothing the top. Bake until a cake tester inserted into the center of the cake comes out clean, 20 to 30 minutes, rotating pan after 10 minutes.

7. Cook cake completely on a wire rack. Using a 4-inch heart-shaped cookie cutter, cut out 12 hearts.

8. Place 4 strips of parchment paper around perimeter of a serving plate or lazy susan. Place 1 layer on the cake plate. Spread a thin layer of frosting on the cake; top with another heart, bottom side up. Cover entire cake with a thin layer of frosting and transfer to refrigerator for 10 minutes. Repeat process with remaining ingredients.

9. Remove cakes from the refrigerator and cover each cake with a generous layer of frosting, smoothing as you go around to create a flat surface.

10. Place chocolate in a pastry bag fitted with a small plain round tip; decorate as desired.