Prepare Beef and Sear: Pat the beef chuck roast chunks dry with paper towels and season generously with salt and pepper. Set your Instant Pot to 'Sauté' mode on high. Add olive oil and once hot, sear the beef in batches until browned on all sides, about 3-4 minutes per side. Remove beef and set aside.
Sauté Aromatics: Add the chopped onion to the Instant Pot and sauté for 3-4 minutes until softened. Add the minced garlic and sauté for another minute until fragrant. Deglaze the pot with a splash of beef broth, scraping up any browned bits from the bottom.
Combine Ingredients: Return the seared beef to the Instant Pot. Add the chopped chipotle peppers, adobo sauce, diced green chiles (if using), remaining beef broth, apple cider vinegar, lime juice, ground cumin, dried oregano, smoked paprika, ground cloves, cayenne pepper, and bay leaves. Stir to combine all ingredients well.
Pressure Cook: Secure the lid on your Instant Pot and set the valve to 'Sealing'. Select 'Manual' or 'Pressure Cook' on high pressure for 60 minutes. Once cooking is complete, allow for a natural pressure release for 15 minutes before carefully turning the valve to 'Venting' to release any remaining pressure.
Shred and Serve: Carefully remove the beef from the Instant Pot and transfer it to a large bowl or cutting board. Discard the bay leaves. Using two forks, shred the beef until it's completely pulled apart. Return the shredded beef to the Instant Pot with the cooking liquid and stir to coat. Serve warm with your favorite toppings.