Place the mushrooms in a large resealable plastic bag with the salad dressing. Seal and marinate for at least 15 minutes.
Preheat barbecue for medium-high heat. Heat the pasta sauce in a saucepan over medium heat and keep warm.
Oil the barbecue cooking grate. Place the mushrooms on the barbecue and cook for 7 to 10 minutes on each side, until lightly toasted.
Preheat grill. Spread the bottom of a shallow baking dish or oven-proof plate with just enough pasta sauce to cover the bottom. Place mushrooms in the dish bottom side up and top with the peppers and remaining pasta sauce. Place 2 slices of cheese on each mushroom and sprinkle with oregano and basil.
Grill for 3 to 5 minutes or until the cheese is melted. Serve hot.