Prepare the Marinade: Toast chilies in a skillet, then soak them in hot water for 15 minutes. Blend with garlic, onion, cumin, oregano, and broth until smooth.
Marinate the Meat: Pour the marinade over the meat and let it sit for at least 2 hours or overnight.
Cook the Meat: Simmer the meat in a pot or pressure cooker until tender, about 3 hours.
Prepare the Consommé: Strain the cooking liquid and adjust seasoning.
Assemble the Tacos: Heat tortillas, dip them in consommé, and fill with shredded meat. Garnish with cilantro and onion.
Serve: Pair with a bowl of consommé for dipping and lime wedges.