Remove stems and seeds from dried guajillo and ancho chiles. Place in a heatproof bowl and cover with boiling water. Let soak for 10-15 minutes until soft and pliable.
Season beef chuck roast generously on all sides with kosher salt and black pepper.
Heat avocado oil in a large skillet over medium-high heat until shimmering. Sear the beef for 4-5 minutes per side until deeply browned. Transfer to slow cooker.
Drain softened chiles and add to blender with chipotle peppers, quartered onion, garlic, diced tomatoes, beef broth, apple cider vinegar, cumin, Mexican oregano, smoked paprika, and ground cinnamon. Blend until completely smooth, about 2 minutes.
Pour chile mixture over beef in slow cooker. Add bay leaves and cinnamon stick. Cover and cook on low for 8 hours or on high for 5-6 hours until beef is fork-tender.
Remove beef to cutting board and shred using two forks. Strain cooking liquid through fine-mesh sieve into large bowl, discarding solids. This is your consommé.
Return about 2 cups of sauce to shredded beef and toss to coat. Let rest for 10-15 minutes to absorb flavors.
To assemble tacos: Dip each corn tortilla in warm consommé. Place in lightly oiled skillet over medium heat. Add shredded oaxaca cheese to one half, then birria beef. Fold in half and cook 2-3 minutes per side until golden and crispy.
Serve immediately with remaining consommé for dipping, topped with fresh cilantro, diced onion, and lime wedges.