Mix salt, pepper, garlic powder, onion powder, oregano, basil, and red pepper flakes. Pat the beef dry and rub the spice mix all over.
Heat olive oil in a large Dutch oven over medium-high heat. Sear the roast on all sides until well browned, about 3–4 minutes per side.
Add sliced onion and smashed garlic to the pot. Stir and scrape up browned bits.
Pour in beef broth, pepperoncini brine, Worcestershire, and toss in bay leaves and a few whole pepperoncini. The liquid should come at least halfway up the roast.
Bring to a gentle simmer, cover, and cook at low heat on the stovetop or in a 300°F (150°C) oven for 2.5–3 hours, until the beef feels fork-tender.
Transfer the roast to a plate. Strain the cooking liquid for a smooth au jus, or leave the onions for extra flavor. Skim excess fat if needed.
Let the beef cool until easy to handle, then wrap and chill for 1–2 hours (or overnight). This step firms the meat so you can slice paper-thin.
Using a sharp knife or slicer, cut the beef into very thin slices against the grain.
Bring the strained au jus to a gentle simmer. Taste and adjust salt and pepper.
Slip handfuls of sliced beef into the hot jus for 1–2 minutes to warm through without overcooking.
Lightly toast the rolls for structure.
Pile on warm beef, spoon over extra jus, and top with giardiniera or sautéed sweet peppers. Add cheese if you like.
Serve with a side of au jus for dipping. Go “wet” by dunking the whole sandwich if you want true Chicago style.