Boil half a cup of beef stock in a small pot. Remove from heat and add dried guajillo and ancho chiles. Cover and let sit for 15 minutes to soften. Blend with garlic, crushed tomatoes, apple cider vinegar, and spices until smooth.

Preheat your oven to 350°F (175°C). Heat olive oil in a heavy Dutch oven over medium-high heat. Season chuck roast beef with sea salt and black pepper, then sear for 4-5 minutes on each side until golden brown. Remove and set aside.

Lower heat and sauté chopped onions in the same pot for 5 minutes until translucent. Stir in chili paste and cook for an additional 2-3 minutes. Gradually add remaining beef stock and water, scraping browned bits. Return seared beef into the mixture and bring to a simmer.

Transfer pot to the preheated oven and braise uncovered for about 2.5 hours until beef is tender enough to shred. Let cool slightly before shredding.

Heat a frying pan over medium heat and dip corn tortillas briefly into warm consomé. Fry for 1-2 minutes on each side. Fill each tortilla with shredded beef and a sprinkle of Oaxaca cheese. Fry again until cheese melts and tortillas are golden brown.

Serve crispy Birria Tacos hot with a small bowl of warm consomé for dipping. Top with fresh cilantro and pico de gallo.