Season the chuck roast with salt, black pepper, smoked paprika, garlic powder, and onion powder.
Heat olive oil in a large pot over medium-high heat. Sear the beef for 3 minutes per side until browned.
Add beef broth, diced tomatoes, tomato paste, apple cider vinegar, cumin, and chili powder to the pot.
Cover and simmer on low heat for 3 to 4 hours until the beef is fork tender. Cook beef to a minimum internal temperature of 145°F with a 3 minute rest for food safety.
Remove the beef and shred with two forks. Reserve 2 cups of the cooking broth for dipping.
Heat a skillet over medium heat and butter one side of each bread slice.
Place 4 slices butter side down onto the skillet. Top each with shredded Oaxaca cheese, shredded beef, mozzarella cheese, and cilantro.
Add the remaining bread slices butter side up.
Cook for 3 to 4 minutes per side until the bread is golden brown and the cheese is fully melted. For the crispiest grilled cheese texture, press the sandwiches gently with a spatula while cooking.
Slice the sandwiches and serve hot with warm reserved broth for dipping. The reserved dipping broth becomes even richer after sitting for a few minutes with the shredded beef juices stirred in.