Season the beef chuck roast on all sides with garlic powder and black pepper. Set the instant pot to saute mode and sear the roast for about 3 minutes per side until a deep golden-brown crust forms on both sides. Remove and set aside.
Pour the beef broth and pepperoncini brine into the pot, scraping up any browned bits from the bottom. Place the seared roast back in and sprinkle the ranch seasoning mix and au jus gravy mix evenly over the top.
Place the butter on top of the roast and scatter the pepperoncini peppers around it. Lock the lid, set the valve to sealing, and cook on high pressure for 60 minutes.
Allow the pressure to release naturally for 15 minutes, then quick release any remaining pressure. Transfer the roast to a cutting board and shred it using two forks - it should fall apart effortlessly.
Return the shredded beef to the pot and stir it into the rich, buttery gravy. Let it sit for 5 minutes so the meat absorbs the sauce. Serve over mashed potatoes, egg noodles, or on hoagie rolls with the pepperoncini and extra gravy spooned on top.