In a large heavy skillet (preferably cast iron), melt the butter over high heat. Add the shaved beef in a single layer. Let it sit for 1–2 minutes without stirring to develop a deep brown sear. Flip, cook for 30 seconds, then remove the meat from the pan.

In the same skillet, add the peppers, onions, and mushrooms. The moisture from the vegetables will deglaze the beef drippings from the pan. Sauté until the onions are golden and the peppers are tender-crisp.

Turn the heat to low. Stir in the softened cream cheese, heavy cream, Worcestershire sauce, garlic, and black pepper. Stir until the cream cheese has melted into a thick, savory sauce that coats the vegetables.

Fold the seared beef back into the vegetable mixture.

Transfer the mixture into a greased baking dish. Lay the slices of smoked provolone across the top, overlapping them slightly to create a complete "shield" of cheese.

Bake at 375°F for 15 minutes. For the final 2 minutes, switch the oven to Broil to get those signature brown, bubbly spots on the cheese.