In a small bowl, whisk together the vinegar, oil, garlic, and rosemary. Place the mushrooms in a large re-sealable plastic bag, or a baking dish, and cover with the marinade. Marinate for at least 1 hour and up to 2 hours.

Preheat the grill to medium.

Remove the mushrooms from the marinade and pat dry. Season both sides with salt and pepper, and place gill sides-down on the grill. Add the Vidalia onion slices to the grill. Cook the mushrooms and onion for 5 minutes, then turn. Arrange the cheese on the gills of each mushroom and continue to cook the mushrooms and onion until tender, about 6 to 8 minutes longer. Open the rolls and lightly toast on the grill, insides down.

Place 1 grilled mushroom inside each bun, top with a grilled onion, and garnish each to taste, with aioli. Divide the watercress among the 4 buns and serve immediately.