Pulse the ham pieces in a food processor until they are coarsely chopped. In a large, deep casserole or Dutch oven, heat the olive oil. Add the chopped ham, beef chuck and cloves and cook over high heat, stirring once or twice, until the meat begins to brown, about 10 minutes.
Add the celery, carrot, onion and garlic to the casserole and cook, stirring, until the vegetables are barely softened, about 3 minutes. Stir in the sage, rosemary and crushed red pepper and cook until fragrant, 2 to 3 minutes. Add the red wine and cook until it is nearly evaporated, about 10 minutes. Add the tomato puree, chicken stock and sugar, season with pepper and bring to a boil over moderately high heat. Simmer uncovered over low heat, stirring occasionally, until the sauce is thick and reduced by half, about 45 minutes.
Meanwhile, in a large pot of boiling salted water, cook the orecchiette until al dente.
Stir the heavy cream into the bolognese sauce and simmer for 5 minutes. Stir in the chopped chestnuts and parsley and season lightly with salt. Drain the pasta and transfer to a large bowl. Spoon the bolognese sauce over the pasta and serve, passing the Parmesan on the side.