Set Instant Pot to Sauté mode. When Instant Pot is hot, add oil and continue heating until oil is hot and shimmery.
When oil is hot, add chuck roast. Sear roast 6 minutes or until well-browned, then flip roast over and sear on other side 6 additional minutes. When both sides are well-browned, transfer chuck roast to large plate and set aside.
With Instant Pot still set to Sauté, pour in 1 ½ cups water to deglaze pot. Use wooden spoon or spatula to scrape up any browned bits that might be stuck to bottom of pot and stir to incorporate.
Sprinkle packet of au jus gravy mix into pot and stir well to combine. Once combined, return seared chuck roast to Instant Pot. Note: roast does not need to be fully submerged in water.
Sprinkle ranch dressing mix over chuck roast, then top roast with whole pepperoncini peppers. Place pats of butter directly on top of pepperoncini.
Secure lid on Instant Pot with vent in Sealing position. Set Instant Pot to Manual High Pressure for 55 minutes. Pot will pressurize, then cook time will begin.
When 55 minute cook time ends, immediately (and carefully) Quick Release pressure. Remove lid from pot and set aside.
Use tongs to carefully remove chuck roast from Instant Pot and transfer to cutting board. Do not discard cooking jus from pot.
Using 2 forks, shred chuck roast into small-to-medium-sized pieces. Pick out and discard any large pieces of fat. Continue process until entire roast has been shredded, then set roast aside.
Skim as much fat as possible from cooking jus in Instant Pot and discard. When satisfied, return shredded chuck roast to Instant Pot and stir well to fully coat meat in jus.
Divide pot roast into desired portions and serve warm with mashed potatoes or other preferred sides.