Toast chiles: In a dry skillet, toast guajillo, ancho, and chipotle chiles over medium heat for 1-2 minutes until fragrant. Soak in 2 cups hot water for 15 minutes.
Make sauce: Drain chiles and blend with onion, garlic, oregano, cumin, vinegar, and 1 cup beef broth until smooth.
Prep beef: Cut beef into chunks, season with salt and pepper, and place in a slow cooker.
Cook birria: Pour chile sauce over beef, add remaining broth, cinnamon stick, and bay leaves. Cook on low for 6-8 hours until tender.
Shred meat: Remove beef, shred, and reserve consomé. Skim fat from consomé.
Assemble tacos: Dip a tortilla in consomé, place in a hot skillet, add beef and cheese, fold, and fry for 2-3 minutes per side until crispy.
Serve: Garnish with cilantro and onion. Serve with consomé and lime wedges.