Preheat the oven to 375 degrees.  Bring a large pot of salted water to a boil for the pasta.  Butter a 9-by-13-inch baking dish.  Sprinkle with the bread crumbs, and tap to coat the interior of the dish, tapping out the excess.  Run the pork shoulder through the coarse holes of a meat grinder.  (You can also use pre-ground pork or sausage, but the coarsely ground texture is preferred).

In a food processor, combine the onion, carrot, celery, and garlic.  Process to make a smooth pestata.  To a large Dutch oven over medium-high heat, add the olive oil.  When the oil is hot, add the pestata, and cook until it dries out and is light golden, about 5 minutes.  Add the ground pork, and season with the salt and crushed red pepper.  Reduce the heat to medium, and cook until the pork releases its juices, about 7 minutes.  Increase the heat to get the juices boiling, and cook until they are reduced away and the pork is browned, about 5 minutes.  Add the white wine, and cook until reduce by half, about 2 minutes.  Add the tomatoes, slosh out the can with 1 cup pasta water, and add that, too.  Bring to a simmer, and cook until the pork is tender, about 30 minutes.

Add the zucchini, and cook until it is tender and the sauce is thick, about 20 minutes more.

When the zucchini is almost done, cook the pasta in the boiling water until just al dente (they will cook more as they bake).  Drain, reserving 1 cup pasta water.  In a medium bowl, toss the mozzarella and grated Grana Padano together.  

When the sauce is ready, add the elbows and toss to coat the pasta in the sauce, adding a splash of pasta water if it seems dry.  Remove the pot from the heat, and fold in half of the cheese mixture. Spread the pasta in the prepared pan, and sprinkle with the remaining cheese mixture.  Bake until the sauce is bubbly and the top is brown and crusty, about 25 minutes.  Let it sit 5 minutes before serving.