Add the beef, deglazed liquid, guajillo and pasilla peppers, cinnamon stick, bay leaves, onions and tomatoes to an instant pot or dutch oven. Add enough beef broth to cover everything (2-3 cups). Bring the pot to a boil, then lower the heat and let the pot simmer for 1 hour. You can use the simmer function if you’re using an instant pot. If you want to speed things up, cook it on the pressure-cook setting for about 20 minutes.
Transfer the peppers, tomato, onion and cinnamon stick to a blender with about 1/2 cup of the cooking liquid, the vinegar, lime juice and remaining herbs and seasonings (oregano, cumin and cloves). Puree on high speed for about 30 seconds to 1 minute.
Preheat your oven to 325°F and strain the puree over the meat using a fine mesh sieve. Discard any skins, and seeds left behind in the sieve. Pour the last cup of beef broth over the roast, and cover it with a lid. Transfer the roast to the oven and braise for 1 and 1/2 hours. If you’re using an instant pot, cook it on the pressure-cook setting for about 45 minutes to an hour.
Remove the beef and shred it! The beef should be tender enough that you only have to press it with a fork to shred it. Shred/break apart all of the meat and set it in a casserole dish. Toss the meat in a small amount of Birria (consomé) and cover it with plastic wrap until you’re ready to use it.