Put the meat, quartered onions, smashed garlic and thyme in a large pot and cover with water by one inch. Bring to a boil, reduce the heat and simmer for 2 to 4 hours or until the meat is falling apart. Keep the meat covered with water until it is almost done. At that point you can let the liquid boil off a bit. Drain the meat, reserving the liquid. Strain the liquid and set aside. Discard the onions and garlic. When the meat is cool enough to handle, shred, discarding any bits of fat and bone and set aside.