Heat oven to 375°F. On ungreased cookie sheet, place buns, cut sides up. Bake 5 to 8 minutes or until toasted.
Meanwhile, in 12-inch nonstick skillet, heat oil over medium-high heat. Cook onion and bell pepper in oil 3 minutes, stirring constantly. Add broccoli and mushrooms; sprinkle with basil and seasoned salt; add water. Cover; cook 3 to 5 minutes, stirring occasionally, until broccoli is crisp-tender.
Cut eight 16x12-inch pieces of foil. Spray foil with cooking spray. Drizzle dressing over cut sides of toasted buns. Cut cheese slices to fit sandwiches. Layer Havarti cheese, vegetable mixture and Cheddar cheese in buns. Wrap each sandwich in foil.
Bake 10 to 15 minutes or until warm and cheese is melted.