Preheat the oven to 375 degrees F. Grease a 9-inch casserole with butter.
Bring 6 quarts of water to a boil and add 2 tablespoons salt. Set up an ice bath next to the stovetop. Plunge the chicory into the boiling water and cook until wilted, about 3 minutes, then drain, and plunge into the ice bath. Drain again and squeeze out excess water.
Chop the chicory finely and place in a small saucepan with 1/2-cup chicken stock. Cook over medium-high heat for 5 minutes, then remove from heat, and set aside.
In a medium mixing bowl, beat the eggs, add salt and pepper, to taste, and then add 2 tablespoons each of Parmigiano-Reggiano and caciocavallo. Mix well, then add the chicory.
Turn the mixture into the prepared casserole and top with half of the remaining cheese. Bake in the oven for 30 minutes, until golden brown and crusty. Remove from the oven and allow to cool.
Cut into six wedges and place each in a soup bowl. Bring the remaining chicken stock to a boil. Meanwhile, heat the olive oil to 325 degrees F in a tall-sided pot and add the bread cubes. Fry until they are golden brown on all sides and remove from the oil with a slotted spoon. Drain on paper towels, then distribute evenly among the bowls. Fill each bowl with a ladle of chicken stock, top with the remaining cheese, and serve.
In a large, heavy-bottomed saucepan, heat the oil over high heat until smoking. Add all the chicken parts and brown all over, stirring to avoid burning. Remove the chicken and reserve. Add the carrots, onions, and celery to the pot and cook until soft and browned. Return the chicken to the pot and add 3 quarts of water, the tomato paste, peppercorns, and parsley. Stir with a wooden spoon to dislodge the browned chicken and vegetables bits from the bottom of the pan. Bring almost to a boil, then reduce heat and cook at a low simmer until reduced by half, about 2 hours, occasionally skimming excess fat. Remove from heat, strain, and press on the solids with the bottom of a ladle to extract out all liquids. Stir the stock to facilitate cooling and set aside. Refrigerate stock in small containers for up to a week or freeze for up to a month.
Yield: 1 1/2 quarts