Prepare the Birria:
In a dry skillet over medium heat, toast the dried chiles until fragrant, about 1-2 minutes per side. Be careful not to burn them.
Place the toasted chiles in a bowl and cover with hot water. Let them soak for about 20 minutes until softened.
In the same skillet, add the quartered onion, garlic cloves, and tomatoes. Roast until they develop a slight char, approximately 5 minutes.
Drain the soaked chiles and transfer them to a blender along with the roasted vegetables, cumin seeds, oregano, ground cloves, and 1 cup of beef broth. Blend until smooth.
Cook the Birria:
Season the beef chunks with salt and pepper.
In a large pot or Dutch oven, heat a bit of oil over medium-high heat. Sear the beef pieces until browned on all sides.
Pour the chile sauce over the beef, ensuring the meat is well-coated. Add the bay leaves and the remaining beef broth.
Bring to a boil, then reduce the heat to low. Cover and let it simmer for about 3 hours, or until the meat is tender and easily shreds with a fork.
Once cooked, remove the beef pieces and shred them. Strain the cooking liquid to serve as the consommé.
Assemble the Enchiladas:
Preheat your oven to 375°F (190°C).
Dip each corn tortilla into the warm consommé to soften it.
Place a portion of the shredded birria meat onto each tortilla, sprinkle with a little cheese, and roll them up.
Arrange the rolled tortillas seam-side down in a baking dish.
Pour some consommé over the top of the enchiladas and sprinkle with the remaining cheese.
Bake:
Bake in the preheated oven for about 15-20 minutes, or until the cheese is melted and bubbly.
Serve:
Garnish with chopped cilantro and diced onions.
Serve with lime wedges and additional consommé on the side for dipping.