Add the beef: Place the chuck roast pieces in the Instant Pot, arranging them in an even layer as much as possible.
Add the liquid and seasonings: Pour the beef broth and pepperoncini juice over the roast. Sprinkle the au jus mix and dry ranch dressing mix evenly over the beef. Do not stir. (It's okay if it's only partially submerged.)
Add the pepperoncini and butter: Arrange the whole pepperoncini over the beef, then place the butter slices on top.
Pressure cook: Lock the lid in place and set the valve to Sealing. Cook on High Pressure for 60 minutes. The Instant Pot will take additional time to come to pressure before the cooking time begins.
Naturally release the pressure: When the 60-minute cooking time is complete, leave the Instant Pot undisturbed for 15 minutes to allow the pressure to release naturally.
Release the remaining pressure: After 15 minutes, carefully turn the valve to Venting to release any remaining pressure. Wait until the pin drops completely before opening the lid.
Check the beef: Test the roast with a fork; it should be very tender and pull apart easily. Transfer the beef to a platter and cover loosely to keep warm. If the beef is still tough, lock the lid back in place, set the valve to Sealing, and cook on High Pressure for another 5–10 minutes. Carefully release the pressure before opening the lid and check again for tenderness.
Make the cornstarch slurry: Whisk the cold water and cornstarch together in a small bowl until completely smooth.
Make the gravy: Set the Instant Pot to Sauté. Gradually whisk the cornstarch slurry into the cooking liquid, adding only as much as needed to reach your desired consistency. Cook, whisking frequently, until the gravy thickens, then turn off the Instant Pot.
Serve: Shred the beef or break it into large pieces. Spoon the warm gravy over the roast and serve.