Trim visible large sections of fat from roast, then cut roast into 6-8 large pieces. Season beef with 1/2 tsp each salt and pepper.
Add vegetable oil to Instant Pot and select "Saute". When hot, add beef and cook for a minute or so on each side, until browned. Depending on the size of your beef, you may need to do this in batches.
Remove browned beef to a plate and add onion. Saute for 2-3 minutes, until soft.
Add in 1 cup beef broth and scrape the bottom of the pot with a wooden spoon to remove any browned bits. Add in tomato paste, green chiles and bay leaves.
Press "Cancel - or Keep Warm/Cancel". Return browned beef to the pot and pour pureed chipotle sauce over the top. Top with both halves of the lime.
Close lid securely and make sure the valve is set to "sealing". Select "Manual" or "Pressure Cook" and adjust the +/- button until it reads 60 minutes.
When finished cooking, carefully turn the valve to "venting" for a quick pressure release. When the steam has all escaped, and the pin has dropped, remove the lid and discard bay leaves.
Remove beef pieces to a large bowl and shred, discarding any purely fat parts.
Toss shredded beef with as much of the cooking liquid as you'd like.