Cut beef into thin slices; sprinkle with salt and pepper.
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 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.
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 thick. Remove from heat. Add cheeses and mustard, stirring until smooth. Keep warm (mixture will thicken as it cools).
Hollow out top and bottom halves of hoagie rolls, leaving a 1/2-inch-thick shell; reserve torn bread for another use. Divide beef mixture evenly among bottom halves of hoagie rolls. Drizzle sauce evenly over beef mixture; replace top halves.