Season the meat with salt and pepper and drizzle all over with EVOO.
Place a large Dutch oven over medium-high heat with two turns of the pan of EVOO. Add the pork to the pan and brown all over, about 4-5 minutes on each side. Remove the pork to a platter and add the onion, celery, carrots, garlic and bay leaves to the pot and saute for 3-5 minutes. Add the water to the pot (the liquid should come two-thirds of the way up the pork) and scrape the bottom of the pot to loosen the brown bits. Add the cilantro or parsley and oregano. Bring to a boil, then reduce the heat to simmer. Cover and cook for 2 1/2-3 hours, or until fork tender. Turn off the heat and let rest for 30 minutes. Remove the pork to a shallow platter and shred with forks; cover and reserve.
Strain the braising liquid and return it to the pot. Reduce over medium-high heat until slightly thickened, about 30 minutes more.
Meanwhile, place a deep saute pan over medium-high heat with two turns of the pan of EVOO. Add the bell peppers, onion, garlic, and Fresno chili pepper to the EVOO and season with cumin, oregano, salt and pepper. Cook for about 8-10 minutes, or until softened. Add the cilantro or parsley, olives and tomato paste and stir for another minute. Deglaze the pan with the reduced braising liquid and stir in the tomatoes. Add in the shredded pork and simmer for a few more minutes to allow the pork to soak in the sauce.
Serve the Puerco Ropa Vieja as sliders with 3-inch split rolls or as soft tacos with small charred flour tortillas. Top the pork with red onions dressed with lime juice and pickled jalapeno peppers, for garnish.