Warm a large heavy-bottomed pot or Dutch oven over MED-HIGH heat. Add 1 Tbsp of oil and 1 Tbsp of butter, allowing the butter to melt. Spread the steak slices in a single layer and cook undisturbed for 1 minute. Stir and cook for another 30 seconds to 1 minute until done, then transfer to a plate.

Add the remaining oil and butter to the hot pot. Add the mushrooms, onion, and green pepper. Cook, stirring occasionally, for about 5 minutes until vegetables are tender and mushrooms are browned. Season with thyme, salt, and pepper.

Pour in the beef broth and water, bringing it to a boil. Add the pasta, reduce the heat to maintain a gentle boil, and cook for 12-15 minutes, stirring frequently to prevent sticking.

When most of the liquid is absorbed, turn off the heat. Stir in the sour cream, cream cheese, cooked steak, and half of the chopped provolone until well combined. Adjust seasoning with salt and pepper if needed.

Top the pasta with the remaining chopped provolone and broil for 2-3 minutes until the cheese is melted and gooey. Garnish with black pepper and minced parsley, if desired, and serve hot.