In a small bowl, season the shaved steak with salt, pepper, and onion powder, then toss with 2 tablespoons of the all-purpose flour.
Heat a large skillet over medium heat. Add the olive oil then the seasoned meat. Sear the meat on one side without stirring, then flip and sear on the second side. Add the Worcestershire sauce and stir the meat well. Continue to cook until completely browned. Remove the meat from the pan and set aside.
Melt 1 tablespoon of butter in the skillet, then add the sliced onions. Saute until soft and beginning to brown. Add a pinch of sugar and continue to cook until caramelized. This process takes 8-10 minutes in total. Remove the onions from the pan and set aside.
Melt 1 tablespoon of butter in the skillet, then add the sliced mushrooms. Cook, stirring occasionally, until soft and beginning to brown. Add the dried thyme and minced garlic; stir well. Cook for 1 minute, then stir in the remaining 2 tablespoons of all-purpose flour and cook for 1 minute.
In a large soup pot or Dutch oven, combine the caramelized onions, cooked mushroom mixture, and the beef stock or broth. Bring the soup to a simmer over medium heat and cook for 10 minutes. Add the cooked steak and continue to simmer the soup for 5 minutes.
Cut the center out of the bread bowls. Place them on a foil lined baking sheet and ladle the soup into the bowls. Top each with a slice of provolone cheese. Set the oven to broil then place the baking sheet of bread bowls under the broiler, broiling just until the cheese is melted and beginning to brown.
Serve the soup bowl immediately.