Preheat the oven: Set to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Sauté the veggies: Heat 1 tablespoon oil in a large skillet over medium-high. Add onions and peppers with a pinch of salt.
Cook 5–7 minutes until softened and lightly browned. Add mushrooms and cook 3–4 minutes more. Stir in garlic for 30 seconds.
Transfer to the baking dish.
Cook the steak: In the same skillet, add the remaining oil. Increase heat to high. Season steak with salt, pepper, and smoked paprika.
Sear in batches for 1–2 minutes per side until just cooked. Do not overcook. Add Worcestershire and toss.
Layer steak over the veggies.
Make the creamy binder: In a small bowl, whisk cream cheese and heavy cream until smooth. If stiff, microwave the cream cheese 10–15 seconds first. Season lightly with salt and pepper.
Assemble the casserole: Drizzle the cream mixture evenly over steak and veggies.
Sprinkle mozzarella on top. Lay provolone slices to cover the surface.
Bake: Place in the oven for 12–15 minutes, until cheese is melted and bubbling at the edges.
Optional broil: For browned, blistered cheese, broil 1–2 minutes. Watch closely.
Rest and garnish: Let sit 5 minutes to set.
Top with chopped parsley if you like. Serve hot.