Cook the ground beef, onion, green pepper, and salt in a large skillet over medium-high heat, crumbling the meat, until the beef is no longer pink. Drain excess grease.
Sprinkle the cornstarch over the beef mixture and stir until the meat is evenly coated.
Add the beef broth, steak sauce, and steak seasoning. Stir and bring to a boil.
Reduce the heat to medium-low and simmer for 10 minutes, stirring occasionally, until thickened. The mixture will thicken further off the heat.
While the meat simmers, preheat the broiler. Arrange the split buns on a baking sheet, spread them lightly with butter, and broil for 1–2 minutes until toasted. Watch closely.
Spoon the beef mixture onto the bottom buns. Place provolone on the top buns and broil briefly until the cheese melts.
Close the sandwiches and serve warm.