To begin, toast the dried chillies (guajillo, ancho, and pasilla) in a dry skillet over medium heat for about 1-2 minutes until fragrant, being careful not to burn them. Transfer the chillies to a bowl of hot water to soak for 10 minutes until softened.

While the chillies soak, place the garlic, onion, cumin, cinnamon, oregano, thyme, black pepper, vinegar, and salt into a blender. Drain the softened chillies and add them to the blender as well. Blend until smooth, forming a rich, aromatic marinade.

Place the beef or goat pieces into a large bowl and pour the Chile marinade over them, making sure to coat each piece thoroughly. Cover and refrigerate for at least 4 hours, or ideally overnight, to allow the flavors to develop.

Preheat your oven to 160°C (320°F). Transfer the marinated meat into a large oven-safe pot or Dutch oven. Pour the broth over the meat, adding the cinnamon stick, cloves, and bay leaves. Stir gently to combine, ensuring the meat is mostly submerged in the liquid.

Cover the pot with a lid and place it in the oven. Cook the birria for 3 to 4 hours, or until the meat is tender and easily shreds with a fork. Check periodically to ensure the liquid doesn’t evaporate too much, add more broth or water if necessary.

Once the meat is fully cooked and tender, carefully remove the pot from the oven. Discard the cinnamon stick, cloves, and bay leaves. Shred the meat using two forks, mixing it back into the broth.

Adjust the seasoning by adding more salt, if needed. If you prefer a spicier broth, you can blend some of the cooking liquid with additional soaked chillies and stir it back into the stew.

To serve, ladle the birria into bowls and garnish with fresh cilantro and chopped onions. Serve with lime wedges on the side for a burst of acidity. Enjoy with warm corn tortillas for dipping, or use the meat to make tacos, topping them with more cilantro, onions, and a squeeze of lime.