Remove stems and seeds from the dried guajillo and ancho chiles.
Toast the chiles lightly in a dry pan until fragrant, then soak them in hot water for 15 minutes.
In a blender, combine softened chiles, garlic, onion, chipotle, cumin, coriander, oregano, cinnamon, tomato paste, vinegar, and a splash of broth. Blend until smooth.
Sear the beef in a Dutch oven until browned on all sides.
Pour the blended sauce and remaining broth over the beef, season with salt and pepper.
Cover and simmer on low for 3 hours until the beef is tender and shreds easily.
Remove beef and shred it. Strain the sauce through a fine-mesh sieve for a smooth birria consommé.
Dip corn tortillas into the consommé, fill with shredded beef and cheese if using, and fold.
Fry each taco in a hot skillet with oil until crispy on both sides.
Serve with chopped onion, cilantro, lime wedges, and a side of consommé for dipping.