Step 1: Prepare the Meat

1. Rinse the meat under cold water and pat dry with paper towels.
2. Season the meat lightly with salt.
3. In a large pot or Dutch oven, combine the meat, onion, garlic, bay leaves, and water. Bring to a boil, then reduce the heat to a simmer. Skim off any foam that rises to the top.

Step 2: Toast and Soak the Chilies

1. Heat a skillet over medium heat and toast the chilies for 30 seconds on each side until fragrant.
2. Transfer the toasted chilies to a bowl and cover with hot water. Let them soak for 15 minutes until softened.

Step 3: Make the Chili Sauce

1. Drain the chilies and place them in a blender along with the roasted tomatoes, garlic, cumin, oregano, smoked paprika, cinnamon, vinegar, and beef broth. Blend until smooth.
2. Strain the sauce through a fine-mesh sieve to remove any solids, creating a silky consistency.

Step 4: Cook the Birria

1. Add the chili sauce to the pot with the meat and stir to combine. Simmer on low heat for 3–4 hours, or until the meat is tender and easily shreds with a fork.
2. Taste and adjust the seasoning with salt as needed.

Step 5: Serve

1. Remove the meat from the pot and shred it into bite-sized pieces.
2. Serve the meat in bowls with the broth, garnished with cilantro, diced onion, and lime wedges.