Dump the chuck roast, beef broth, garlic, italian seasoning, salt, pepper, and pepperoncini peppers with juice to the pot of the electric pressure cooker.
Place the lid on the electric pressure cooker and set the valve to sealing. Set the pressure cooker to “manual” or “pressure cook” for 60 minutes. Allow a natural release of pressure when the cook cycle is complete.
Meanwhile, place a medium skillet over medium-high heat. Add the olive oil. When it is hot, add the sliced bell pepper. To caramelize the edges of the bell pepper, stir only as needed.
Shred or thinly slice the beef.
Serve the beef on sliced hoagie rolls topped with sliced provolone cheese and bell peppers and the au jux on the side for dipping.