Cut the short rib meat off the bone and cut into large chunks and place on a large sheet pan. Cut the chuck roast and add to the sheet pan. Set aside.
In a small bowl, combine the salt, garlic powder, smoked paprika and Mesquite seasoning. Generously season the meat with the seasoning mixture. Set aside for about 30 minutes.
In a stock pot, add the chilis, onion, garlic cloves, tomatoes and bay leaves. Cover with water and bring to a hard simmer over medium-high heat for about 15 minutes, or until the peppers are tender.
Meanwhile, in a large cast iron skillet, heat tablespoon of oil over medium- high heat. Sear the meat in small batches, adding 1 tablespoon of oil each time, about 5 minutes per batch. Remove the meat from the skillet and place in a Dutch oven.
Return to the boiling chilies and strain the contents from the water and add to a blender.
To the blender, add the oregano, cumin, coriander, cloves, cinnamon, apple cider vinegar and 1 cup beef broth. Blend until smooth. Note: you may have to blend in batches, if it won’t all fit in your blender at one time.
Stir the contents of the blender into the beef and stir in the remaining 2 cups of beef broth. Cook over medium-high heat for 10 minutes, at a low boil, stirring occasionally.
Cover the dish and place in a preheated oven to 350 degrees F. for about 2 ½ to 3 hours, or until the meat shreds easily.
Remove the meat from the sauce, shred and set in a warm place.
Take a tortilla and dip in the red broth, to coat. Place in a cast iron skillet over medium-low heat, and cook for about 1 to 2 minutes, or until it warms through. Flip and add about 2 heaping tablespoons of meat to one side of the tortilla, followed by 1 to 2 tablespoons each of the Oaxaca and mozzarella cheeses. Fold the tortilla over and mash slightly with the spatula. Continue cooking until the cheeses have melted and taco has warmed through. Place in a warm oven and repeat with the remaining ingredients.
Let cool slightly and serve with the leftover red sauce for dipping