1. Place beef in freezer for 15 minutes. Cut beef across the grain into thin slices. Sprinkle beef with salt and pepper. Remove brown gills from the undersides of mushroom caps using a spoon; discard gills. Remove stems; discard. Thinly slice mushroom caps; cut slices in half crosswise.
2. Heat a large nonstick skillet over medium-high heat. Add 1 teaspoon oil to pan; swirl to coat. Add beef to pan; sauté 2 minutes or until beef loses its pink color, stirring constantly. Remove beef from pan. Add remaining 1 teaspoon oil to pan. Add onion; sauté 3 minutes. Add mushrooms, bell pepper, and garlic; sauté 6 minutes. Return beef to pan; sauté 1 minute or until thoroughly heated and vegetables are tender. Remove from heat. Stir in Worcestershire and soy sauce; keep warm.
3. Place flour in a small saucepan; gradually add milk, stirring with a whisk until blended. Bring to a simmer over medium heat; cook 1 minute or until slightly thickened. Remove from heat. Add cheeses and mustard, stirring until smooth. Keep warm (mixture will thicken as it cools).
4. Hollow out top and bottom halves of bread, leaving a 1/2-inch-thick shell; reserve torn bread for another use. Divide the beef mixture evenly among bottom halves of hoagies. Drizzle sauce evenly over beef mixture; replace top halves.