Preheat your oven to 300F. Pat the pork dry with paper towel, cut it into large (about 2-inch) pieces and sprinkle with salt and pepper. Set a Dutch oven over medium-high heat, add a drizzle of oil and brown the meat well on all sides. Move it over to one side and add the onion to the pan; cook for a few minutes, until they’ve softened and loosened some of the browned bits from the bottom of the pan. Add the garlic and cook for another minute or two.
Add the diced and crushed tomatoes and thyme, cover and braise for 3 hours, or until the meat is very tender. Add the gnocchi along with 1/2 cup water (unless it’s already very saucy), stir to coat well with sauce and return it to the oven for half an hour, until the gnocchi is tender. Pull the meat apart with forks and serve topped with Parmesan cheese. Serves 6.