Toast the guajillo and ancho chiles in a dry skillet over medium heat for about 30 seconds per side until fragrant. Transfer them to a bowl, cover with boiling water, and let them soak for 15 minutes until softened.
Drain the chiles and add them to a blender along with the fire roasted tomatoes, onion quarters, garlic, apple cider vinegar, cumin, oregano, ground cloves, black pepper, and salt. Blend until completely smooth.
Place the beef chuck pieces into the instant pot. Pour the chile sauce and beef broth over the meat, then nestle in the bay leaves. Lock the lid, set the valve to sealing, and cook on high pressure for 45 minutes.
Let the pressure release naturally for 15 minutes, then quick release any remaining pressure. Remove the bay leaves and transfer the beef to a cutting board. Shred the meat using two forks and return it to the pot, stirring it into the rich consomme broth.
Dip each corn tortilla into the consomme from the pot, then pan fry them in a skillet over medium-high heat until the edges are crispy. Fill each tortilla with the shredded birria and serve with a small bowl of warm consomme on the side, topped with fresh cilantro, diced onion, and a squeeze of lime.