Heat a large dutch oven or heavy-bottomed pot over medium-high heat. Add 1 tablespoon olive oil and 1 tablespoon butter, and allow the butter to melt.
Add steak slices in an even layer, and cook for 2 minutes, stirring occasionally. Set steak aside on a plate.
Add the remaining 1 tablespoon of olive oil and 1 tablespoon of butter to the dutch oven. Add mushrooms, onion, and green pepper. Cook for 5 minutes, stirring occasionally, or until the vegetables are tender and the mushrooms are slightly browned. Season with thyme.
Pour in beef broth and water, and bring to a boil. Add spiral pasta, and reduce heat so liquids are at a slow boil. Cook for 12-15 minutes. Stir pasta frequently to prevent it from sticking to the bottom of the pot.
When most of the liquid has been absorbed, turn off the heat. Stir in sour cream, cream cheese, steak, and provolone cheese. Stir until all the ingredients are well combined.