Slice the partially frozen meat into very thin slices. Mix together the chili powder, oregano, garlic, salt and pepper in a small bowl. Toss the meat slices in the mixture to coat.
Heat the oil in heavy saute pan (such as cast iron) over medium heat. Cook the onions and peppers until tender, about 5 minutes. Add the mushrooms and cook until all the vegetables are soft and golden, about 5 minutes longer.
Preheat the broiler to high.
Remove the vegetables to a plate and add a splash more oil to the pan. Raise the heat to medium-high. Cook the meat quickly in the hot pan, browning on both sides. Once brown, reduce the heat to low and mix together the vegetables and beef. Add the cream cheese, Worcestershire sauce and American cheese, and stir until creamy and well incorporated. Split open the hoagie rolls and place on a baking sheet. Divide the beef mixture among the rolls and top with the mozzarella cheese. Broil until the cheese begins to bubble, 1 to 2 minutes. Watch carefully for burning. Serve.