Place the cubed beef in a large bowl and cover it with water. Add the vinegar and let it soak for 15 minutes. Drain, rinse thoroughly, and pat the beef dry with paper towels.
Season the beef with soy sauce, crushed garlic, adobo, dried oregano, and lime juice. Toss to coat evenly, then cover and marinate in the refrigerator for at least 1 hour.
Heat the oil and sugar in a Dutch oven or cast aluminum pan (caldero), over medium heat. Stir occasionally and let the sugar caramelize until it turns brown.
Add the beef to the pan, flipping it as needed until browned on all sides.
Add the tomato paste and toss the beef to coat it evenly.
Add 1 cup of water, bring to a simmer, then let the meat cook (uncovered) for 15-20 minutes.
Once the liquid has reduced by half, add about ½ cup of water to keep the meat covered, and let it simmer for another 15-20 minutes. Repeat this process as needed, adding just enough water each time, until the meat is tender and easily breaks apart with a fork. This process can take anywhere from 45 minutes to an hour.
Add the sliced peppers and onions, then top off with a little more water to create enough sauce and keep the meat from drying out. Cover and let it simmer for 5-10 minutes more, or until the vegetables are tender but still slightly firm.
Turn off the heat, then stir in the cilantro. Cover and let it sit for a few minutes. Serve with rice, beans, and a green salad.