In a large skillet over medium-high heat, cook the ground beef, breaking it up until browned and cooked through. Drain excess fat, leaving a little for flavor.
Add the onion, green bell pepper, and red bell pepper to the skillet. Cook until softened and slightly caramelized.
Stir in the garlic, Worcestershire sauce, salt, black pepper, garlic powder, and onion powder. Cook until fragrant.
Lower the heat, layer provolone cheese over the beef mixture, cover, and let melt completely.
Brush hoagie rolls with melted butter and toast until golden.
Scoop the cheesy beef mixture onto the toasted rolls and serve warm.