Pat chuck roast dry and season with salt and freshly ground black pepper all over. In a Dutch oven over high heat, heat oil until shimmering. Brown beef on all sides until a deep brown crust develops, about 10 to 15 minutes.
In the bottom of a slow cooker, add onion, pepperoncini, and gardiniera. Add 2 cups of broth. Nestle browned roast on top of vegetables.
Add the garlic, basil, oregano, and thyme directly on top of the beef roast. Cover and cook on high until meat is extremely tender and falling apart, about 5 to 6 hours.
Remove the beef to a rimmed baking sheet and shred with 2 forks, discarding any gristle or large pieces of fat. Set aside.
Pour the juice and vegetables through a fine mesh strainer. Let the juice settle for a few minutes, then spoon off as much visible fat as possible. Discard vegetables.
Transfer the juice to saucepan, add remaining 2 cups beef broth, and bring to a boil. Reduce heat and simmer until reduced by 1/3, about 5 to 7 minutes. Remove from heat.
To serve, spread the buns with butter and toast in a dry skillet until golden brown, about 3 to 5 minutes. Brush each bun with au jus, then top with shredded beef. Add 1 slice of provelone to each sandwich. Garnish with giardiniera, pepperoncini, and serve with the remaining au jus on the side, for dipping.