Soften the chiles: In a dry skillet, toast guajillo, ancho, and arbol chiles over medium heat for 30–60 seconds until fragrant. Add them to a bowl and cover with hot water, letting them soak for 15 minutes until rehydrated.
Make the sauce: Blend the softened chiles (with about ½ cup of soaking water), onion, garlic, tomatoes, beef broth, vinegar, chili powder, cumin, oregano, cinnamon, salt, and pepper until smooth.
Brown the beef: Heat the oil in a Dutch oven over medium-high heat. Sear the beef chunks for 2–3 minutes per side until browned and caramelized, adding depth to the dish.
Braise the beef: Pour in the blended sauce and add bay leaves. Bring this tantalizing mixture to a simmer. Cover and cook on low heat for 2 ½–3 hours or place it in a 300°F oven until the beef becomes tender and shreds easily.
Shred and reserve consommé: Once cooked, remove the beef, shred it with two forks, then return it to the pot. Skim away excess fat into a bowl (you’ll use this to fry tortillas). Keep the broth as the dipping consommé.
Crisp the tacos: Heat a griddle or skillet over medium heat. Dip a tortilla in the reserved orange-red fat for added flavor, then place it on the hot skillet. Load it with cheese, shredded birria, and a spoonful of salsa roja (if you’re using it). Fold and cook for 2–3 minutes per side until crispy and melty.
Finish and serve: Top your tacos with diced onion and cilantro. Serve with hot consommé for dipping and lime wedges for an irresistible explosion of flavor.
Notes
Make the birria a day in advance for deeper flavors. Consider customizing toppings to suit your tastes.