Heat a dutch oven, or large heavy bottomed pot, over MED HIGH heat. Add 1 Tbsp oil and 1 Tbsp butter and let butter melt. Add steak slices in an even layer. You may need to cook this in batches, depending on the size of your pot. Let steak cook undisturbed for 1 minute, then stir around for about 30 seconds to 1 minute more. Don't cook any longer or they'll be too overcooked. Remove steak to a plate.
Add remaining 1 Tbsp of oil and 1 Tbsp of butter to hot pot, then add mushrooms, onions and green pepper. Cook, stirring occasionally, 5 minutes or so, until tender and mushrooms have browned. Season with thyme and a pinch of salt and pepper.
Pour in beef stock and water, bring to a boil. Add pasta, reduce heat so liquid is at a gentle boil, and boil for approximately 12-15 minutes. Stir pasta frequently to prevent uneven cooking and pasta sticking to the bottom of the pot.
When most of the liquid has been absorbed, turn off the heat. Add sour cream, cream cheese, cooked steak slices, and half the chopped provolone slices. Stir to combine well. Taste, and add salt and pepper if needed.
Top pasta with remaining chopped provolone and broil for 2-3 minutes, until cheese is melted and gooey. Sprinkle with black pepper and minced parsley (optional), and serve hot.