Preheat the oven to 375°F (190°C).
Lightly grease a 9x13-inch casserole dish.
Warm 1 tablespoon oil in a large skillet over medium-high heat. Add the onions and peppers with a pinch of salt. Cook, stirring, until softened and lightly golden, about 6–8 minutes.
Transfer to a plate.
Add the remaining oil to the skillet. If using mushrooms, sauté them with a pinch of salt until they give off their liquid and brown slightly, 4–5 minutes. Add to the pepper-onion mixture.
Add the ground beef to the same skillet.
Season with salt, pepper, onion powder, garlic powder, and paprika. Cook, breaking it up with a spatula, until browned and no pink remains, about 6–8 minutes. Drain excess fat if needed.
Stir in the minced garlic and cook 30 seconds until fragrant.
Add Worcestershire, beef broth, heavy cream, Dijon, and cream cheese. Reduce heat and stir until the cream cheese melts and the sauce thickens slightly, 2–3 minutes. Taste and adjust seasoning.
Return the peppers, onions, and mushrooms to the skillet.
Stir to coat everything in the creamy sauce.
Transfer the mixture to the prepared baking dish. Top evenly with shredded mozzarella and then layer the provolone slices across the top for that classic, melty finish.
Bake for 12–15 minutes, until the cheese is melted and bubbling around the edges. For extra browning, broil 1–2 minutes, watching closely.
Let rest 5–10 minutes.
Garnish with chopped parsley if you like, then slice and serve.