Toast the ancho, guajiilo, and arbol chilies. Transfer to a pot of hot water. Cover and allow to steep for 20 minutes.
Remove the chilies from the water and discard the stems and seeds. Puree the chilies in the blender with one cup of warm water. Set aside.
Season all the meat generously with black pepper and kosher salt. Add oil to a large dutch oven over medium heat. Sear all sides of the meat in batches, 2 minutes per a side. Take the meat out and set aside.
Add more oil to the pot and sauté the onions briefly. Once softened, add the tomato paste and cook for approximately 3 minutes or until the paste darkens.
Add the garlic, beef, beef stock, and lime juice to the pot. Season the pot with the ground cumin and Mexican oregano. Bring to a boil, reduce the heat and allow to cook for 1 hour.
Using a cheesecloth add in the coriander seeds, fresh black peppercorn, cinnamon stick, thyme, bay leaves. Tie the cheesecloth tightly.
Place the cheesecloth and pureed chilies into the pot. Cover the pot and simmer the mixture for 2-3 hours with occasional stirring.
Remove the meat and any bones from the stew. Chop up the meat.
Season the stew with salt and black pepper.