Preheat your oven to 300°F.
Pat the chuck roast dry with paper towels. Season generously with salt and black pepper.
Heat olive oil in a large Dutch oven over medium-high heat. Sear the roast for about 3–4 minutes per side, until nicely browned. Transfer the roast to a plate.
In the same Dutch oven, add the sliced onion and bell peppers. Sauté for 5 minutes, stirring occasionally, until softened.
Stir in the minced garlic, Italian seasoning, and crushed red pepper flakes (if using). Cook for 1 more minute.
Pour in the beef broth and pepperoncini juice, scraping up any browned bits from the bottom of the pot.
Return the roast to the Dutch oven. Nestle the pepperoncini peppers around the meat.
Cover with the lid and transfer the Dutch oven to the oven. Braise for 3½ to 4 hours, or until the beef is fall-apart tender and shreds easily with a fork.
Remove the beef from the pot and shred it with two forks. Return the shredded beef to the pot and stir it into the juices.
Serve the Italian beef warm on hoagie rolls, with a ladle of extra juices if you like it "wet." Top with provolone cheese if desired.