To start, you will need to brown your meat first. Heat the oil in a frying pan over medium-high heat. Meanwhile, season your beef with some salt and pepper. Then, cook the meat over high heat until it is beautifully brown on all sides. You don't have to cook them. They only need to get some color and flavor. Set the browned meat aside for later.
Next, in a large pot or directly into your slow cooker, heat some more oil and add your onions. Sautee them over medium heat for roughly 2 minutes, then add the carrots, celery, and red bell pepper. Give these ingredients a good stir and cook them for another 2 minutes.
Once your vegetables have started to sweat, add the garlic and tomato paste. Allow them to cook for a minute while stirring constantly. It will help coat the vegetables nicely.
Now, add all of your browned meat with your spices and dried herbs. You don't have to cook these for very long. But make sure to mix them properly.
Finally, add the chopped tomatoes, beef stock, and white wine. Mix all the ingredients well and bring them to a boil.
Once your liquid is boiling, reduce the heat to a very low simmer. Cover the pot and allow the Cuban Ropa Vieja to cook for 3-4 hours. The meat has finished cooking when it falls off the fork.
To shred your cooked meat, remove any large vegetable chunks from the saucy mixture. Then, transfer the cooked meat to a plate. Shred the meat pieces using two forks.
Once shredded, return the meat to the sauce and simmer it over medium heat until you have a thicker consistency. Add the fresh cilantro and serve the Cuban Ropa Vieja while it's still hot.