In a large enameled cast-iron casserole, heat the olive oil. Add the carrot, celery, onion and garlic and cook over moderate heat, stirring occasionally, until softened but not browned, about 10 minutes. Add the pancetta and ground beef and cook, breaking up the meat with a wooden spoon, until no longer pink, about 8 minutes. Add the tomato paste and cook over low heat, stirring occasionally, until shiny and rust-colored, about 10 minutes.
Add the diced ham, milk, white wine and water to the casserole and simmer the ragù over moderately low heat, stirring occasionally, until it is thick and saucy, about 1 hour and 15 minutes. Season the ragù with salt and pepper.
In a large pot of boiling salted water, cook the fusilli, stirring often, until al dente. Drain the fusilli and add it to the sauce. Stir well to coat the pasta. Transfer the pasta to shallow bowls and serve right away, passing grated pecorino at the table.