01 - Preheat oven to 325°F (163°C). 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 lightly smoking. Sear the seasoned roast on all sides until a deep golden-brown crust forms, approximately 2-3 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 2-3 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. Stir well, scraping up all browned bits from the bottom of the pot.
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 easily shreds 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 pot with the strained au jus and simmer gently over low heat for 5-10 minutes, allowing the meat to absorb the flavorful broth.
08 - Split the Italian rolls lengthwise. Pile the juicy sliced beef generously onto each roll. Ladle extra au jus over the top. Finish with a hearty spoonful of giardiniera and roasted sweet peppers. Serve immediately with additional au jus on the side for dipping.