Toss the beef with the Italian seasoning, 1/2 teaspoon salt and a few grinds of pepper. Scatter the mushrooms and garlic in a 6- to 8-quart slow cooker; top with the beef. Add the pepperoncini, brine, tomatoes and beef broth. Cover and cook on low until the beef is tender, 8 hours.
Uncover the slow cooker and let stand 5 minutes. Spoon off any fat from the top and discard. Shred the beef with 2 forks.
Meanwhile, cook the polenta as the label directs. Remove from the heat and stir in the parmesan and butter until smooth; season with salt and pepper. Divide among bowls and top with the beef mixture.