Prepare the chiles: Remove the stems and seeds from the dried guajillo, ancho, and pasilla chiles. Toast the chiles in a dry skillet over medium heat for about 1–2 minutes until fragrant.

Soak the toasted chiles: Once toasted, soak the chiles in hot water for 20 minutes to soften them.

Roast the vegetables: Roast or char the Roma tomatoes, onion, and garlic in a skillet over medium heat until they develop a nice char, about 5–7 minutes.

Blend the sauce: In a blender, combine the drained soaked chiles, roasted tomatoes, garlic, onion, cumin, cloves, cinnamon stick, oregano, vinegar, and 1 cup of beef broth. Blend until completely smooth.

Prepare the meat: Cut the beef chuck roast and short ribs into large chunks, and season with salt and black pepper.

Sear the beef: Heat the neutral oil in a Dutch oven over medium-high heat, then sear the beef chunks for about 3-4 minutes on each side.

Combine and simmer: Pour the blended chile sauce over the seared beef and add bay leaves and the remaining beef broth. Stir to blend.

Slow cook the birria: Reduce the heat to low and let cook for 3 to 4 hours.

Shred the meat: Remove the meat and shred, then return it to the pot to simmer uncovered for an additional 15 minutes.

Serve and garnish: Ladle the rich birria into bowls, and serve with fresh cilantro, diced onion, and lime wedges.