01 - Preheat oven to 325°F. Position the rack in the lower third of the oven 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. Coat the roast on all sides with the spice mixture, pressing firmly to adhere.
03 - Set a large Dutch oven or heavy oven-safe pot over medium-high heat until it begins to shimmer. Place the seasoned roast in the pot and sear on all sides until a deep golden-brown crust forms, 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, stirring occasionally to loosen the fond from the bottom of the pot.
05 - Pour in the beef broth, water, and Worcestershire sauce. Add the Italian seasoning, sliced green bell pepper, and fennel seeds. Scrape up any remaining browned bits from the bottom of the pot to incorporate into the liquid.
06 - 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 2½ to 3 hours, or until the beef is fork-tender and easily shreddable.
07 - Remove the roast from the pot and let 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 using a spoon or fat separator.
08 - Thinly slice the rested beef against the grain, using a sharp knife or meat slicer for the finest results. Return the sliced beef to the strained au jus and simmer gently for 5 to 10 minutes, allowing the meat to absorb the flavorful broth.
09 - Split the rolls lengthwise and pile the sliced beef generously onto each. Ladle extra au jus over the top. Finish with a heaping spoonful of giardiniera and roasted sweet peppers. Serve immediately with additional au jus on the side for dipping.