**Prepare the Beef:** Heat 1 tablespoon of olive oil in a large pot over medium-high heat. Sear the thinly sliced beef until browned and cooked through. Remove from the pot and set aside.

**Cook Vegetables:** In the same pot, add the remaining olive oil. Sauté the onion, bell peppers, and mushrooms (if using) until softened, about 5 minutes. Add the minced garlic and cook for another minute.

**Create the Base:** Sprinkle the flour over the vegetables and stir well to coat. Gradually whisk in the beef broth to prevent lumps. Bring the mixture to a simmer.

**Add the Cream and Seasoning:** Stir in the heavy cream, smoked paprika, salt, and pepper. Allow the soup to simmer for 10 minutes to thicken.

**Melt the Cheese:** Lower the heat and add the shredded provolone and mozzarella cheeses. Stir until the cheese is fully melted and incorporated into the soup.

**Combine Beef and Serve:** Return the cooked beef to the pot and stir to combine. Ladle the soup into bowls, garnish with extra shredded cheese if desired, and serve with crusty bread or croutons on the side.