How to Make It
Preheat the oven to 275°. In a large skillet, melt the butter. Add the garlic, carrots, onions and celery and season with salt and pepper. Cover and cook over low heat, stirring occasionally, until the vegetables are softened but not browned, about 10 minutes.
Season the pork all over with salt, pepper and the thyme leaves. In a medium enameled cast-iron casserole, heat the oil. Add the pork and sear it over moderate heat until browned on all sides. Transfer the pork to a platter and discard the fat in the casserole; wipe the casserole clean. Return the pork to the casserole, meaty side up.
Spoon the vegetables around the meat and add the stock and bunches of thyme sprigs. Cover with a sheet of buttered wax paper and a lid and bring to a boil on the stove. Transfer the casserole to the oven and braise the pork, basting every 30 minutes, for about 3 hours, or until the pork is very tender.
Remove the casserole from the oven. Carefully transfer the meat to a carving board and season it generously with salt and pepper. Cover loosely with foil and let stand for about 15 minutes. Strain the cooking juices through a fine sieve into a gravy boat. Thickly slice the pork and serve with the cooking juices.