In a large pot or Dutch oven, heat the vegetable oil over medium-high heat. Add the beef cubes and brown them on all sides, about 5-7 minutes. Remove the beef and set aside.
In the same pot, add the diced onion and sauté until translucent, about 3-4 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
Add the chopped tomatillos, jalapeño peppers, cumin, oregano, salt, and black pepper to the pot. Stir well to combine.
Return the browned beef to the pot and pour in the beef broth. Bring the mixture to a boil, then reduce the heat to low and cover. Simmer for 1.5 to 2 hours, or until the beef is tender.
Once the beef is tender, stir in the chopped cilantro and lime juice. Adjust seasoning if necessary.
Serve hot, garnished with additional cilantro if desired.