Preheat your oven to 375 degrees Fahrenheit. In a bowl, combine the 2 pounds of lean ground beef with 2 eggs and mash it all together until well mixed. Get a cake pan (around 6.5 x 9 inches or a small round one) and rub a little olive oil into it to prevent sticking. Press the meat mixture firmly into the prepared cake pan. Cook in the preheated oven at 375 degrees for 25 to 30 minutes. Once done, remove from the oven and let it rest until it cools completely. Carefully remove all drippings. For the icing, spread a thin layer of 100% natural peanut butter (ensure no artificial sweeteners) over the cooled meat cake. Decorate the cake with some carrot slices before serving to your dog.