01 - Preheat oven to 325°F. Position the rack in the lower-middle position for even heat distribution.
02 - Pat the beef chuck roast thoroughly dry with paper towels. Rub evenly with olive oil. In a small bowl, combine kosher salt, black pepper, dried oregano, dried basil, garlic powder, and crushed red pepper flakes. Press the spice mixture firmly onto all surfaces of the roast.
03 - Set a large Dutch oven or heavy oven-safe pot over medium-high heat until shimmering. Sear the seasoned roast on all sides until deeply browned, approximately 2 to 3 minutes per side. Transfer the roast to a plate and set aside.
04 - In the same pot, add the sliced onion and minced garlic. Sauté for 2 to 3 minutes until softened and fragrant. Pour in the beef broth, water, and Worcestershire sauce. Add the Italian seasoning, sliced green bell pepper, and fennel seeds. Scrape up any browned bits from the bottom of the pot to deglaze.
05 - Return the seared roast to the pot, nestling it into the liquid. Cover tightly with a lid or heavy-duty foil and transfer to the preheated oven. Braise for 2.5 to 3 hours, or until the beef is fork-tender and easily pulls apart.
06 - Remove the roast from the pot and let it rest on a cutting board for 15 minutes. Strain the cooking liquid through a fine-mesh strainer into a bowl, discarding the solids. Skim off any excess fat from the surface of the au jus.
07 - Using a sharp knife or meat slicer, thinly slice the rested beef against the grain. Return the sliced beef to the strained au jus and simmer gently over low heat for 5 to 10 minutes, allowing the meat to absorb the flavorful liquid.
08 - Split the rolls or hoagie buns and pile the sliced beef generously onto each. Ladle extra au jus over the meat. Top with giardiniera and roasted sweet peppers to taste. Serve immediately with additional au jus on the side for dipping.