Cut beef round steak into thin slices and brown briefly in a hot pan for color.
Add browned beef, green peppers, onion, beef stock, garlic salt, black pepper, and Italian dressing mix to the crock pot. Stir to combine.
Cover and cook on Low for 8 hours, until beef is tender.
Line a baking sheet with foil or parchment.
Spoon the beef and vegetable mixture onto sliced hoagie buns.
Top each sandwich with 2 slices of provolone cheese, overlapping as needed.
Bake at 350°F or broil on low for a few minutes, just until the cheese melts.
Serve warm.
Notes
Brown the beef briefly before slow cooking if you have time; it adds more flavor than adding raw beef straight to the crock pot. Use a slotted spoon when filling buns so they do not get soggy. The beef mixture can be made a day ahead and reheated before assembling sandwiches. Leftovers keep refrigerated for up to 4 days.