In a large skillet, heat the olive oil over medium heat. Add the diced onion and green bell pepper, cooking until softened, about 5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.

Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and no longer pink, about 6-8 minutes. Drain any excess fat.

Stir in the beef broth, Worcestershire sauce, soy sauce, and Dijon mustard. Season with salt and pepper to taste. Bring the mixture to a simmer and cook for about 10 minutes, allowing the flavors to meld and the sauce to thicken slightly.

While the beef mixture is simmering, preheat your oven broiler. Split the hamburger buns and place them on a baking sheet, cut side up. Toast under the broiler for 1-2 minutes until lightly golden.

Once the beef mixture is ready, spoon it generously onto the toasted buns. Top each with 2 slices of provolone cheese. Return the baking sheet to the broiler and cook for an additional 2-3 minutes, or until the cheese is melted and bubbly.

Remove from the oven, garnish with chopped parsley if desired, and serve immediately.