Heat olive oil in a large pot or Dutch oven over medium heat. Add chopped onion and both bell peppers, cooking for 8-10 minutes while stirring occasionally. You're looking for softened vegetables with golden-brown edges and a slightly sweet aroma.

Increase heat to medium-high and add the thinly sliced steak. Cook for 5-6 minutes total, stirring frequently, until the meat develops a nice brown crust. Work in two batches if needed to avoid overcrowding.

Pour in the beef broth and diced tomatoes with their juices, scraping up any browned bits from the bottom of the pot. Stir in Worcestershire sauce, thyme, and red pepper flakes if using. Season with salt and pepper.

Bring the mixture to a gentle simmer, then reduce heat to low. Cover and let it simmer for 30-40 minutes to allow the flavors to blend.

While the soup base simmers, prepare the cheese sauce. In a medium saucepan, melt butter over medium heat. Whisk in flour and cook for 1-2 minutes, stirring constantly, until the mixture turns light golden and smells nutty.

Gradually add milk about half a cup at a time, whisking thoroughly after each addition until smooth. Continue whisking as the mixture thickens for 5-7 minutes total.

Reduce heat to low and stir in the softened cream cheese until completely melted. Add provolone and mozzarella cheeses gradually, stirring until melted into a smooth sauce. Season with garlic powder, onion powder, salt, and pepper.

Once soup base has finished simmering and cheese sauce is ready, slowly pour the cheese sauce into the pot, stirring constantly. Heat through gently over low heat for 3-4 minutes until steaming hot. Never let it boil.

Taste and adjust consistency if needed by adding more broth to thin or simmering uncovered to thicken. Ladle into bowls and top with extra cheese and fresh parsley. Serve immediately with crusty rolls.