Remove the stems and seeds from the dried guajillo and ancho chiles. In a large skillet over medium heat, toast the chiles briefly for about 2-3 minutes, until they fragrant but not burned. Then, soak the toasted chiles in hot water for 15-20 minutes until they soften, making them ready for the sauce.

In a blender, combine the soaked chiles, garlic cloves, chopped onion, cinnamon stick, cloves, cumin, oregano, and beef broth. Blend everything on high until you reach a smooth consistency, which should take about 1-2 minutes.

Season the beef chuck roast generously with salt and pepper. In a Dutch oven, sear the roast in a drizzle of oil over medium-high heat for about 4-5 minutes on each side until browned. Next, pour in the blended chile sauce and additional beef broth as needed, add bay leaves, and bring to a gentle simmer. Cover and cook for 2.5 to 3 hours until the meat is tender and falling apart.

Once the beef is cooked, carefully remove it from the pot and place it on a cutting board. Using two forks, shred the beef into bite-sized pieces, allowing the flavor to seep in.

Warm the corn tortillas on a dry skillet for about 30 seconds on each side until pliable. Keep them covered in a clean kitchen towel to retain warmth and moisture while you prepare the rest of the ingredients.

Start assembling the Birria Enchiladas by placing a generous amount of shredded beef in the center of each tortilla. Roll them tightly, tucking in the sides as you go, and place them seam-side down in a greased baking dish.

Pour the reserved enchilada sauce evenly over the assembled enchiladas, ensuring each one is well-coated. Sprinkle a generous layer of shredded cheese on top.

Preheat your oven to 375°F (190°C). Bake the enchiladas in the preheated oven for around 15-20 minutes, or until the cheese has melted and is bubbly.

Once baked, remove the enchiladas from the oven and let them rest for a few minutes. Top each serving with crumbled Cotija cheese and freshly chopped cilantro.