Soak the guajillo and ancho chiles in hot water for about 30 minutes, or until softened.
In a blender, combine the soaked chiles, garlic, toasted cumin seeds, oregano, ground cloves, ground cinnamon, salt, and black pepper. Add about 1 cup of beef broth and blend until smooth.
Heat vegetable oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Sear the beef chuck roast chunks on all sides until browned.
Pour the chile sauce over the beef. Add the remaining 3 cups of beef broth. Bring to a simmer, then cover and reduce heat to low.
Cook for 3-4 hours, or until the beef is very tender and easily shredded.
Remove the beef from the pot and shred it using two forks. Return the shredded beef to the pot with the sauce.
To assemble the tacos, lightly fry the corn tortillas in a little of the birria fat or oil from the pot until slightly crispy.
Spoon a generous amount of shredded birria meat onto each tortilla. Top with chopped cilantro and diced onion.
Serve immediately with the consommé for dipping and lime wedges on the side.
Notes
For an even richer consommé, you can skim off some of the fat from the top of the birria after it has cooked and use it to fry the tortillas.