In a 12 to 14-inch saucepan, combine 1/2 cup of olive oil, and onions. Cook until soft. Season the pork with salt and pepper and add to onions. Cook until deep brown. Add tomato paste, tomato sauce, and chicken stock. Bring the mixture to a boil over high heat, stirring well to combine. Season, to taste, with salt. Turn the heat to low and let simmer until the meat becomes very tender, about 1 hour to 1 hour 30 minutes, stirring every 15 minutes. If the sauce becomes too thick, add some extra chicken stock or water. Throughout the cooking process, the meat should always be just covered in sauce.
In the meantime, bring 12 cups of water to a boil in a saucepan, and add 1/2 teaspoon of salt. Add the rice and cook, stirring occasionally, over medium-high heat, covered, until the rice is al dente, about 25 minutes. Drain the rice and place it in a large, shallow bowl. Allow the rice to cool for at least 30 minutes.
When the meat sauce is done and the rice is cool, stir the beaten eggs into the rice. Mix well to combine. Stir 3/4 of the meat ragu, 1/2 cup freshly grated cheese, and the nutmeg into the rice. Season the mixture, to taste, with salt and pepper. Mix again to combine and then set the mixture aside.
Bring 6 quarts of water to a boil and add 2 tablespoons salt. Add the penne, and cook the pasta according to the package directions, until al dente. While the pasta cooks, melt 6 tablespoons of butter in a small saucepan. Remove from the heat. Drain the pasta, reserving 1 cup of the cooking liquid.
Place the drained pasta in a bowl. Add 1 cup of the meat ragu, 1 cup pecorino, the melted butter, the hot pepper flakes, and 1/2 cup of the bread crumbs. Season the mixture, to taste, with salt and pepper and stir well to combine.
Preheat the oven to 375 degrees F.
Generously butter the sides and bottom of a round 12 to 14-inch baking dish with 4-inch sides. Add 3/4 cup bread crumbs to the dish, turning and rotating the dish so that the bread crumbs coat all of the sides.
Spoon 1/3 of the rice into the dish, spreading the to form an even layer across the bottom of the dish. Top the rice with 1/2 of the pasta. Use a wooden spoon to gently smooth the pasta so that it to forms an even layer across the top. Spoon 1/2 of the ragu over the pasta. Top with another layer of rice (1/2 of what remains), followed by the remaining pasta, then the remaining ragu. Cover the ragu with the remaining rice, and use a wooden spoon to smooth the rice across the top so that it forms an even layer. Sprinkle the top of the rice with remaining 1/4 cup of bread crumbs and sprinkle the remaining 2 tablespoons of oil and caciocavallo atop the bread crumbs. Bake until golden brown, about 30 minutes. Remove the timbale from the oven and allow to cool 10 minutes.
To unmold the timbale, run the blade of a thin knife around the inside edge of the pan separate any sticking ingredients. Place a round serving plate, one that is 6 inches larger than the baking pan over the timbale. Being careful to keep the platter in contact with the baking dish, and not allowing the dish to slip on the platter, invert the baking dish over the platter. Gently remove the baking dish, leaving the timbale on the platter. If the timbale does not slide out easily, don't tug or try to force it out. Instead, wipe the bottom and the sides of the baking dish with a hot kitchen towel. If necessary, carefully shake the platter and dish in unison, being careful not to separate one from the other. The timbale should now release easily when the dish is lifted. Allow the timbale to rest 10 minutes before serving. The dish can be simply served as is, with a big serving spoon or cut into wedges, topped with remaining ragu, more cheese and chili flakes.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic and cook until soft and light golden brown, about 8 to 10 minutes. Add the thyme and carrot and cook 5 minutes more, until the carrot is quite soft. Add the tomatoes and juice and bring to a boil, stirring often. Lower the heat and simmer for 30 minutes until as thick as hot cereal. Season with salt and serve. This sauce holds 1 week in the refrigerator or up to 6 months in the freezer.