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. Combine kosher salt, black pepper, dried oregano, dried basil, garlic powder, and crushed red pepper flakes in a small bowl. 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 rippling hot. Sear the seasoned roast on all sides, approximately 2 to 3 minutes per side, until a deep golden-brown crust forms. 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 heavy lid or foil. Transfer to the preheated oven and braise for 2.5 to 3 hours, until the beef is fork-tender and pulls apart easily.
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, slice the rested beef thinly 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 flavors.
08 - Split the rolls open and pile the sliced beef generously onto each. Ladle extra au jus over the top. Finish with a generous spoonful of giardiniera and roasted sweet peppers. Serve immediately with additional au jus on the side for dipping.