Let the 3-4 pound chuck roast sit out at room temperature for 15 minutes. Generously season the roast all over with salt.
Heat a large skillet over medium-high heat, then add 3 tablespoons vegetable oil. When hot, sear the roast on all sides until golden brown. Cook long enough to develop a crust, about 10 minutes total. Transfer to the slow cooker.
Add a splash of beef broth to the skillet and deglaze the pan. Then, pour 1 cup low sodium beef broth and the pan fond over the beef.
In a small bowl, mix 1 tablespoon Italian seasoning, 1 tablespoon granulated sugar, 2 tablespoons salt, 1 ½ teaspoons garlic powder, 1 teaspoon onion powder, ½ teaspoon black pepper, and ½ teaspoon dried parsley. Sprinkle all over the beef.
Add 4 ounces pepperoncini pepper slices and ¼ cup pepperoncini brine to the slow cooker.
Cover and cook on LOW for 10 hours - flip the roast over halfway through if you're able.
Shred the beef in the slow cooker using 2 forks. Mix everything together and cook for another 30 minutes on LOW.
To serve, split open 1 hoagie rolls and stuff with beef. Top with ¼ cups giardiniera (or more to taste), and 2 slices provolone cheese if using. Repeat with the remaining ingredients and serve warm.
