Season the beef with a teaspoon of salt, a pinch of black pepper, thyme, and oregano. In a large cast aluminum or cast iron pot, heat half of the vegetable oil. Sear the meat throughout (be careful with splatters, you're trying to cook the beef, not yourself). Add enough water to cover the meat and cover the pot with a tight-fitting lid. Simmer over low heat until the meat is very tender (it will start to flake). Rotate the meat every once in a while for even cooking. Add water if necessary to prevent it from becoming too dry. By the end, there should be about three cups of liquid remaining. Let it cool to room temperature.
Once the meat is cool enough to handle, cut it into slices no more than two inches wide and shred the meat with your hands.
In a heavy saucepan, heat the remaining vegetable oil and cook and stir the onions until they become translucent. Add the garlic, carrots, and red bell pepper and simmer over very low heat for three minutes.
Add the tomatoes and simmer for about ten minutes until tender.
Add the vinegar and tomato sauce along with the shredded meat and any remaining liquid. Simmer for ten minutes over low heat, or until all the vegetables are cooked through. Taste and season with salt to taste if needed.
