To make the croutons, preheat the oven to 400°. In a large bowl, toss together bread cubes, olive oil, salt and pepper. Spread into an even layer on a 15x10x1-in. baking sheet. Bake 6-8 minutes or until golden brown; set aside to cool.
To make the soup, heat olive oil in a large soup pot over medium-high heat. Add steak; season with salt and pepper. Cook until browned on all sides. Use a slotted spoon to remove the steak; set aside.
Remove all but 1 tablespoon of fat from the soup pot; discard remaining. Add mushrooms; cook until most of the liquid has evaporated. Add onion, red pepper and green pepper; cook until tender, 6-8 minutes. Add garlic; cook until fragrant, 30-60 seconds. Stir in flour; cook until golden, 2-3 minutes, stirring occasionally.
Stir in beef broth, heavy cream, Worcestershire sauce and Italian seasoning. Bring to a simmer; cook until slightly thickened, 15-20 minutes. Reduce heat to low; stir in shredded provolone, a small handful at a time, until melted. Add the steak back in; simmer an additional 5 minutes.
Spoon the soup into bowls. Top with minced parsley, additional shredded provolone and hoagie croutons.