01 - Preheat the oven to 325°F (163°C).
02 - Pat the beef chuck roast dry with paper towels. Rub evenly with olive oil. In a small bowl, combine the kosher salt, black pepper, dried oregano, dried basil, garlic powder, and crushed red pepper flakes. Coat the roast thoroughly on all sides with the spice mixture.
03 - Heat a large Dutch oven or heavy oven-safe pot over medium-high heat. Sear the seasoned roast on all sides until deeply browned, approximately 2–3 minutes per side. Remove the roast and set it aside on a plate.
04 - In the same pot, add the sliced onion and minced garlic. Sauté over medium heat for 2–3 minutes until softened and fragrant, scraping up any browned bits from the bottom of the pot.
05 - Pour in the beef broth, water, Worcestershire sauce, Italian seasoning, sliced green bell pepper, and fennel seeds. Stir well, bringing the liquid to a gentle simmer while deglazing the pot.
06 - Return the seared roast to the pot, ensuring it is partially submerged in the liquid. Cover tightly with a lid and transfer to the preheated oven. Braise for 2½ to 3 hours, or until the beef is fork-tender and pulls apart easily.
07 - Carefully remove the roast from the pot and let it rest 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.
08 - Thinly slice the rested beef against the grain using a sharp knife or meat slicer. Return the sliced beef to the pot with the strained au jus and simmer over low heat for 5–10 minutes, allowing the meat to absorb the flavors.
09 - Split the rolls or hoagie buns and pile the hot 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.