Start by removing the stems and seeds from the dried guajillo, ancho, and chipotle peppers.
In a large pot, toast the peppers over medium heat for a few minutes until fragrant. Be careful not to burn them.
Once toasted, place the peppers in a blender along with the quartered onion, minced garlic, ground cumin, dried oregano, black pepper, salt, and enough beef broth to blend. Blend until smooth.
In the same pot, add the beef chuck roast and pour the blended sauce over the meat. Add the bay leaf and remaining beef broth, ensuring the meat is covered.
Bring the mixture to a boil, then reduce the heat to low, cover, and let simmer for about 2 to 3 hours, or until the meat is tender and easily shreds with a fork.
Once cooked, remove the beef from the pot and shred it using two forks. Set it aside.
To serve, heat corn tortillas in a skillet until warm and pliable. Fill each tortilla with shredded birria meat and top with chopped cilantro and diced onion.
Serve with lime wedges and a small cup of the reserved broth for dipping.
For a spicy kick, leave some of the seeds in the chipotle peppers.
You can make the broth ahead of time and refrigerate it; the flavors deepen overnight.
Leftover birria can be stored in the refrigerator for up to 3 days or frozen for up to 3 months.