Place a large pot or Dutch oven over medium-high heat and add olive oil. Season beef chunks with salt and pepper, then sear on all sides until browned. Add half of the onion to the pot, cook for 2 more minutes, then remove from heat.

In a medium pot, combine guajillo chiles, ancho chiles, tomatoes, the other half of the onion, garlic cloves, cinnamon stick, and bay leaf. Add 4–5 cups water, enough to cover ingredients. Bring to a boil over medium-high heat, then reduce to low and simmer uncovered for 10 minutes.

Add oregano, cumin seeds, thyme, salt, and peppercorns to the chile pot. Stir and simmer for another 10 minutes. Remove from heat and let cool slightly.

Strain the chile mixture through a mesh strainer over a bowl, discarding the cinnamon stick and bay leaf. Transfer solids to a blender, add 2 cups of the strained liquid and 1 cup beef broth, and blend until smooth. Season with salt to taste.

Return the pot with beef to the stove over medium heat. Pour the blended sauce over the beef, adding more broth if needed to cover. Bring to a simmer, then reduce heat, cover, and cook for 2½–3 hours until beef is tender.

Remove beef from the sauce and shred with forks. Skim excess fat from the surface of the sauce if desired—this is your consommé for dipping.

Heat a skillet or griddle over medium heat. Dip tortillas into the top layer of the consommé, place on the skillet, sprinkle with cheese, add shredded beef, fold, and cook until crispy on both sides. Serve with small bowls of consommé for dipping.