Place beef chuck into the bottom of a slow cooker and pour beef broth and Worcestershire sauce over meat.
Season with Italian seasoning, garlic pepper seasoning, and sea salt and place the lid on the slow cooker.
Cook on LOW for 7-8 hours.
Skim fat off the top of the liquid in the slow cooker and use two forks to shred beef.
In a nonstick skillet over medium heat, melt butter and saute onions and bell peppers until tender, about 4-5 minutes.
Add mushrooms and minced garlic and cook, stirring constantly to prevent garlic from burning, for 2-3 minutes.
Add salt and pepper to taste and stir.
Add sauteed vegetables into the slow cooker and stir to combine everything.
Place halved hoagie rolls on a baking sheet. Use a slotted spoon to evenly disperse the beef mixture between the 8 hoagie rolls and top beef mixture with provolone/muenster cheese.
Broil sandwiches in the oven until hoagies are toasted and cheese is melted, about 3-4 minutes.