In a large casserole (that has a tight fitting lid) heat 3 tablespoons oil over medium-high heat. Add the carrots, celery, and 1 onion and fry for a few minutes until softened; remove the vegetables to a plate. Season the meat with salt and pepper; add 2 tablespoons more oil to the pan, if needed, and brown the meat on both sides, about 5 minutes. Return the softened vegetables to the pan along with the bay leaf. Add enough water to just about cover the meat and bring to a boil. Lower heat, cover, and simmer gently until meat is very tender, 1 1/2 to 2 hours. Remove meat from the pot and set aside; strain the liquid and reserve.
Add another 2 tablespoons oil to the pan and put in the peppers, garlic, tomatoes, and the remaining onion; fry on medium-low heat until everything is soft and broken down, about 15 minutes. Shred the meat and add to the pan to heat through. Add some of the reserved braising liquid if the mixture becomes too dry. Serve with Black Beans and cooked white rice, garnish with cilantro leaves.
In a 6-quart pressure cooker over medium-high heat, pour in 3 tablespoons oil. Add the ham hock and onions and cook until the onions are wilted and the ham hock is lightly browned, about 5 minutes. Throw in the garlic and bay leaf and cook for 1 minute more. Add the beans and give a good stir. Pour in the water; add the remaining tablespoon of oil, 1 tablespoon of salt, and a couple of grindings of pepper. Following the manufacturer's instructions, cover, lock the lid, and bring to high pressure. Lower heat to maintain pressure and start timing. Cook at high pressure for 25 minutes. Remove from heat and let rest for 5 minutes. Release the steam, again following the manufacturer's directions. If the beans are underdone, simmer them with the lid off until tender. Remove bay leaf and discard. Pick meat from ham hock and add to beans; discard the bone. Taste and adjust seasoning.
The oil prevents the beans from foaming and clogging the steam vent of the pressure cooker.
Recipe courtesy of Tyler Florence