Tie the meat and season aggressively with salt and pepper. In a Dutch oven, heat the oil over high heat until smoking. Brown the meat on all sides, then add the carrot, onion and celery and cook until vegetables are browned. Add the wine and cook over high heat until the wine has reduced by half, about 5 minutes. Add the tomato puree, bring to a boil, reduce the heat to a simmer and cover the pan. Continue to cook over low heat until the meat is very tender. Remove the meat from the pan and cut it into 1-inch cubes. Set aside in a large mixing bowl. Keep the pan juices warm, and remove any extraneous grease with a ladle.
Preheat the oven to 350 degrees F.
Bring 6 quarts of water to a boil and add 2 tablespoons salt. Cook the ziti in the boiling water according to the package directions, until tender yet al dente. While the pasta is cooking, place the ricotta in a bowl and add a ladle of the pasta cooking water to melt it. Drain the pasta and add it to the bowl with the meat. Add the ricotta and the caciotta and stir to combine.
Brush the insides of a large casserole with extra-virgin olive oil. Place a ladle of sauce in the bottom of the casserole, followed by a layer of the pasta and meat mixture. Grate some of the Parmigiano-Reggiano over, then repeat with another layer of sauce, then pasta and meat, the Parmigiano until all ingredients are used up and casserole is full. Bake in the oven 15 minutes. Serve in warmed pasta bowls.
Recipe copyright 2000, Mario Batali. All Rights Reserved.