1. Make the cake in a 13x9-inch baking pan following instructions on the box of cake mix (Preheat oven to 350 degrees F; mix cake mix, water, oil, and eggs together in a large bowl; pour batter into pan greased generously with shortening.). Allow the cake to cool completely.
2. When cake is cool, make buttercream frosting by first whipping the soft butter in a large bowl with an electric mixer on high speed. Add two cups of the powdered sugar, mix well, then add remaining powdered sugar. Add 1/4 cup of whole milk and vanilla, then mix on high speed for 2 minutes or until frosting is smooth and creamy.
3. Turn cake out of the pan onto wax paper. Using both hands, carefully flip the cake over, so that it's right-side-up, onto another strip of wax paper. Now you're going to cut through the cake twice, creating three layers. We'll start at the bottom slice. First slide the cake over to the edge of your kitchen counter. This way you can drop your hand with the knife down below the counter at the edge to get a nice, straight cut through the cake. Using a long bread knife or other long serrated knife, cut through the bottom third of the cake. Spin the cake and wax paper so that you can cut through all sides (your knife probably won't get all the way through to the other side). When the cake is sliced, carefully flip the top section over onto the other sheet of wax paper. Frost the bottom layer of cake with approximately 1/3 of the buttercream frosting. Break the chilled semi-sweet chocolate into little bits that are a tad smaller than chocolate chips. A good way to do this is to put the chilled chocolate into a large zip-top bag, then use the handle of a butter knife to smash the unsuspecting chocolate into pieces. Sprinkle about 1/3 of the chocolate bits over the frosting on the bottom layer.
4. Turn the top section back over onto the bottom layer. Again, slice through the top section creating the final two layers. Carefully flip the top over onto the wax paper, and frost the new layer as you did with the first layer, adding chocolate bits as well. You may, at this point, wish to slice the top into thirds across the width of the cake. This makes flipping over the top layer much easier. It's also how you're going to slice the cake later, so you'll never see the cuts. Any cracks or breaks are no big deal since you'll just cover up the goofs with frosting.
5. Carefully reassemble the top section on the rest of the cake. If you have a large bulge in the center of the cake, you may wish to slice that off so that the cake is flatter on top. Throw that slice away. Frost the top of the cake with the remaining frosting, then sprinkle on the remaining chocolate bits.
6. The cake is served as triangular slices. So, slice it up by first cutting through the middle of the cake, lengthwise. Next cut across the cake through the middle (widthwise) twice. Now you have six slices that just need to be cut from corner to corner one time each, creating 12 triangular slices. Chill any cake you don't eat that day.