In a large pot, heat the vegetable oil over medium heat. Add the beef chuck roast and short ribs, browning them on all sides for about 5-7 minutes. Remove the meat and set aside.
In the same pot, add the onion and garlic, sautéing until the onion is translucent, about 3-4 minutes.
In a separate bowl, soak the guajillo and ancho chiles in hot water for about 15 minutes until softened. Drain and blend the chiles with 1 cup of beef broth until smooth.
Return the browned meat to the pot and add the blended chile mixture, remaining beef broth, cumin, oregano, paprika, salt, and pepper. Stir to combine.
Bring the mixture to a simmer, cover, and cook on low heat for about 2-3 hours, or until the meat is tender and easily shredded. Alternatively, you can use a slow cooker on low for 6-8 hours.
Once the meat is cooked, shred it using two forks and mix it back into the broth.
To assemble the tacos, heat a skillet over medium heat. Dip each tortilla in the broth, then place it in the skillet. Add a generous amount of shredded meat and top with cilantro and diced onion. Fold the tortilla in half and cook until crispy, about 2-3 minutes per side.
Serve the tacos hot with lime wedges on the side for squeezing over the top.