Season the steak evenly with salt and pepper.
Heat 1 tablespoon of oil in a Dutch oven or large pot over medium-high heat. Add the steak and cook for 5-6 minutes or until the meat is browned and cooked through. Remove the steak from the pan, transfer it to a bowl, and set it aside.
Return the pot to the heat and reduce the heat to medium. Add the remaining tablespoon of oil, onions, peppers, and mushrooms. Cook, stirring regularly, for 10 minutes or until the onions turn translucent and the mushroom moisture has evaporated.
Add the garlic and cook for 1-2 minutes or until the garlic is golden and fragrant.
Stir in the beef broth and Better than Bouillon paste. Increase the heat to medium-high, bring to a simmer, and cook for 10-12 minutes.
While the soup simmers, make the roux. Melt the butter in a medium saucepan over medium heat. Whisk in the flour and cook for 1-2 minutes until the mixture starts to sizzle and get puffy.
Whisk the milk into the roux and cook for 4-5 minutes, whisking occasionally until it thickens. Remove the pan from the heat and stir in the cheese until smooth and melted.
Stir the roux and cooked steak into the soup until well combined. Return to a simmer and cook for 2-3 minutes, stirring occasionally, until thickened and creamy.
Season the soup to taste with salt and pepper. Serve the soup hot, topped with chopped parsley, croutons, and/or shredded provolone cheese.