Heat the olive oil in a large pot over medium-high heat. Pat the beef cubes dry with a paper towel and season them with salt and pepper. Sear the beef in batches, ensuring each piece gets browned on all sides—about 4–5 minutes per batch. Remove the browned beef and set aside.

In the same pot, add the chopped onion. Cook over medium heat until it turns translucent and soft, about 5 minutes. Add the garlic and sauté for 1 more minute, stirring constantly to avoid burning.

Stir in the chopped tomatillos, roasted green chiles, and jalapeño if using. Let everything cook together for 5–7 minutes until the tomatillos soften and begin to break down. You should see the mixture become more saucy and aromatic.

Return the browned beef to the pot. Pour in the beef broth, then stir in the ground cumin and dried oregano. Bring the mixture to a gentle boil, then reduce heat to low. Cover partially and let it simmer for 1.5 to 2 hours, stirring occasionally. The beef should become fork-tender, and the broth rich and flavorful.

Taste and adjust seasoning with more salt and pepper if needed. The stew should be brothy but slightly thick from the breakdown of tomatillos and chiles.

Ladle the Caldillo into bowls. Garnish with fresh chopped cilantro and serve with lime wedges. A squeeze of lime brightens up every bite.