Prepare the Spice Mixture: In a small bowl, combine chipotle powder, paprika, dried oregano, ground All Spice, coriander powder, onion or garlic powder, salt, and pepper. Mix thoroughly.
Season the Beef: Evenly sprinkle approximately four teaspoons of the prepared spice mixture over the beef pieces, ensuring they are fully coated. Pat the spices into the meat to adhere properly.
Brown the Beef: Heat the olive oil in a large, heavy-based pot over high heat. Add the seasoned beef in batches if necessary, searing each piece until well-browned on all sides. Once browned, transfer the beef to a plate.
Sauté the Aromatics: Reduce the heat to medium. If necessary, add additional olive oil to the pot. Add the minced garlic and diced onion, sautéing for approximately three minutes until they are soft and translucent.
Deglaze the Pot: Pour in the orange juice and lime juice. Use a wooden spoon or spatula to scrape the browned bits from the bottom of the pot, incorporating them into the liquid, which adds depth to the flavor.
Simmer the Ingredients: Add the crushed tomatoes, beef or chicken broth, water, and the remaining spice mixture to the pot. Stir well to combine. Return the browned beef to the pot, ensuring it is submerged in the liquid.
Cook the Beef: Cover the pot and bring the contents to a simmer. Reduce the heat to maintain a gentle simmer, allowing the beef to cook slowly and become tender, approximately 2 hours.
Reduce the Sauce: After the beef is tender, remove the lid and continue to simmer for an additional 30 minutes to allow the sauce to reduce and thicken. During this time, remove the beef and shred it using two forks.
Final Reduction: Allow the sauce to simmer uncovered for 10 to 15 minutes to achieve the desired consistency. Season with additional salt as needed. Optionally, purée the sauce with a stick blender for a smoother texture.
Combine and Serve: Return the shredded beef to the sauce, mixing well to ensure the meat is evenly coated. Serve the beef in a large dish, using some of the sauce for drizzling if desired.