Prepare the Birria:
- Prep the meat. Trim and cube the chuck roast and short ribs. Season with salt and pepper. Set aside in a large container with a lid.
- Soften the dried chilis. Bring a medium sized pot of water to boil. Once boiling, remove from heat and soak the guajillo chilis for 10 minutes. Remove the peppers from the water and remove both the stems and seeds.
- Make the marinade. In a blender, place the guajillo peppers, one chipotle pepper, all of the adobo sauce, apple cider vinegar, tomato paste, garlic, oregano, cumin, paprika and cayenne. Blend until smooth.
- Marinate the meat. Pour the sauce over the meat in the container. Cover with the lid and marinate for at least 1 hour.
Cook the Stew
- Preheat the oven to 325F.
- Cook the onion and sear the meat. Drizzle olive oil in the bottom of a french or dutch oven. Heat oil over medium heat and add the chopped onion. Cook for 3 minutes or until softened. Add the marinated meat and all the sauce. Mix in the cinnamon, bay leaves and beef broth.
- Cover and braise the beef in the oven for 3 hours.
- Remove the stew from the oven and skim some of the fat off the top. Place the fat in a separate dish and set aside.
- Remove meat and shred with a fork. Return to the dutch oven once finished. Stir to toss the shredded meat with the sauce.
Assemble the tacos:
- Melt the reserved fat. Add 1-2 tablespoons of the reserved fat into a large skillet over medium-high heat.
- Fry the tacos. One at a time, dip one side of the corn tortillas into the stew and place coated side down onto the heated skillet. Top the tortilla with the shredded Oaxaca cheese. When the cheese is starting to melt, top it off with shredded beef and fold over one side onto the other. Fry on both sides until crispy. Remove and set onto a serving platter. Repeat with the remaining tacos.
Serve! Top the tacos with more Oaxaca cheese and cilantro. Pour some of the birria stew broth into a cup for an easy dipping sauce.