Remove the stems and seeds of all the peppers.
Set a 5-quart pot or dutch oven over medium heat. Put the peppers in the dry pan and toast until aromatic, about 5 minutes. Remove the chilis from the pot.
Add the cooking oil to the pot. Season the beef chunks with salt and pepper, then place them in the pot and sear for 3-4 minutes per side. Transfer beef to a plate.
Add the onion to the pot and saute for 2-3 minutes.
Add the garlic and saute for 30 seconds.
Add the bay leaves, cinnamon stick, oregano, black peppercorns, cumin, coriander, tomato paste, apple cider vinegar, and ginger. Whisk to combine and saute for just 30 seconds.
Pour in the beef stock. Deglaze the bottom of the pot to remove any browned bits.
Return the chilis and beef to the pot. Make sure all the chilis are submerged.
Cover with a lid and cook for 3-4 hours, until the meat is fork tender.
Discard the bay leaf, cinnamon, and ginger. Transfer the beef to a cutting board or bowl and shred with 2 forks.
Blend the liquid and chilis in the pot with an immersion blender. If you don't have one, put some of the liquid and all the chilis in a blender and blend until smooth. Return to the pot.
Add the shredded beef back to the pot. Season with salt and pepper, as needed.
To make tacos, heat a skillet over medium heat. Dip a tortilla into the birria sauce, then place it on the skillet and cook on both sides until slightly toasted.
Add some cheese to one side of the tortilla and some beef to the other. Close the tortilla and cook for 1-2 more minutes, until the cheese is melted.
Transfer to a plate, garnish with onion, cilantro, and lime slices. Serve hot with a bowl of the consommé on the side for dipping.