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 kosher salt, black pepper, dried oregano, dried basil, garlic powder, and crushed red pepper flakes. Coat the roast thoroughly with the spice mixture on all sides.
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 aside on a plate.
04 - In the same Dutch oven, 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 any 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 lid and transfer to the preheated oven. Braise for 2.5 to 3 hours, or until the beef is fork-tender and easily shreds apart.
06 - Carefully 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 in the pot and simmer over low heat for 5-10 minutes, allowing the meat to absorb the flavorful broth.
08 - Split the French rolls or hoagie buns. Pile the au jus-soaked beef generously onto each roll. 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.