Dress meat with oil, salt and pepper. Brown the meat over medium-high heat in a Dutch oven. Add water, cilantro or parsley, oregano, onion, celery, carrots, garlic and bay. Bring to a boil then reduce heat to simmer and cook uncovered for 1 1/2 hours. Turn off heat and let rest for half an hour.
Remove meat to shallow platter and shred with forks, cover and reserve. Strain the braising liquids and return to pot, reduce over medium high heat about 30 minutes more.