Heat a large Dutch oven over medium-high heat for about a minute. Add a drizzle of vegetable oil to coat the bottom. Add the shaved steak, spreading it in a single layer, and season with Worcestershire sauce and 1 teaspoon of garlic salt. Cook the steak, flipping and stirring constantly, until fully cooked, about 2-3 minutes. Transfer the steak to a plate and set aside.
In the same pot, add the remaining vegetable oil and stir in the chopped bell peppers. Cook for about 3 minutes, or until they start to soften. Transfer the peppers to the plate with the steak.
Melt the butter in the pot, then add the diced onions. Cook until the onions begin to soften and deepen in color, then add the minced garlic and cook for another minute.
Sprinkle the flour over the onions and garlic, stirring to create a roux. If the mixture seems dry, add more butter or vegetable oil, one tablespoon at a time. Cook the roux for 3 minutes, stirring constantly.
Gradually add the beef broth, milk, and half-and-half, stirring to avoid lumps. Add the remaining garlic salt, oregano, crushed red pepper flakes, cayenne, and black pepper. Stir in the diced potatoes, making sure they’re fully submerged. Bring the soup to a boil, then reduce heat to medium-low and cover with a lid.
Let the soup cook for 10-15 minutes, stirring occasionally, until the potatoes are fork-tender. If the soup becomes too thick, add more broth or milk to maintain a creamy texture.
Once the potatoes are tender, reduce the heat to low. Using an immersion blender, blend the soup for about 45 seconds to add creaminess while keeping some potato chunks intact. (Blend fully if a smoother consistency is desired.)
Stir in the white American cheese, ensuring it melts completely, then add the provolone, stirring until melted for a deliciously cheesy pull.
Taste the soup and adjust seasonings as needed. Cover and let rest for 5 minutes to meld the flavors. Stir one last time before serving, garnishing with minced parsley or chives if desired.