Using a spoon, scrape and discard the brown gills from the undersides of the mushrooms.
In a large resealable plastic bag, combine the mushrooms and salad dressing. Seal the bag, and turn to coat the mushrooms. Place in the refrigerator and marinate for at least 1 hour or up to 2 hours.
Drain the mushrooms, discarding the marinade. Preheat the grill to medium-high heat (350 to 400 degrees F). Spray the grill rack with cooking spray. Grill the mushroom caps, covered with the grill lid, until tender, 3 to 4 minutes per side. Top each with a slice of cheese. Spread the cut sides of the buns with butter if desired. Place the buns cut-sides down on the grill rack. Grill, covered with the lid, until toasted. Remove from the grill, and spread evenly with Dill-Mustard Sauce. Top with grilled mushrooms and desired toppings. Serve immediately.
In a small bowl, stir together the mayonnaise, mustard, dill, parsley and garlic. Cover and chill for up to 3 days.