Gather all ingredients. Cut the beef chuck roast into large chunks. Place the meat in a large pot with quartered onion and minced garlic.
Add guajillo and ancho chiles, ground cumin, dried oregano, smoked paprika, salt, and black pepper to the pot. Pour in beef broth and water, ensuring the meat is submerged. Stir gently.
Bring the pot to a boil over medium-high heat. Once boiling, reduce heat to low, cover, and let simmer for 120 to 180 minutes until meat is tender.
Remove the meat from the pot and let it cool slightly. Strain the broth and set aside. Shred the meat into bite-sized pieces.
Heat a skillet over medium heat. Dip each corn tortilla in the reserved broth to soften. Place tortilla in skillet, add shredded meat, and sprinkle with cheese if desired. Fold and cook until golden brown and crispy, about 2-3 minutes per side.
Serve the tacos on a platter garnished with chopped cilantro and diced onion, with lime wedges on the side.