Season the pork with salt and pepper. In a large enameled cast-iron casserole, heat the olive oil until shimmering. Add the pork in a single layer and cook over moderately high heat until the pieces are golden brown all over, about 12 minutes. Add the carrots, celery, onion and garlic and cook until softened and browned in spots, about 8 minutes. Add the tomatoes and their juices and bring to a simmer. Add the red wine and thyme sprigs and cook over high heat until the wine is reduced by half, about 5 minutes. Add the stock and bring to a boil. Cover and simmer over low heat until the pork is very tender, about 2 hours.

Using a slotted spoon, transfer the pork and vegetables to a food processor; discard the thyme sprigs. Pulse just until the pork is shredded. Scrape the shredded pork and vegetables back into the casserole. Stir in the chopped parsley, oregano and crushed red pepper and season with salt and pepper.

Preheat the oven to 375 degrees. In a large pot of boiling salted water, cook the orecchiette until it is still firm to the bite, about 5 minutes; drain well. Add the orecchiette to the casserole and toss with the pork sauce. Scrape the pasta into a very large baking dish and sprinkle all over with the Parmigiano-Reggiano. Bake the casserole in the upper third of the oven for about 35 minutes, until golden brown on top and bubbling. Let the baked pasta stand for 10 minutes before serving.

The pork sugo can be refrigerated for up to 2 days. Reheat before tossing with the orecchiette.