Preheat the grill. Season the vegetables with 2 tablespoons of the olive oil, salt, and pepper. Place all the vegetables on the grill (except for the mushrooms) and grill for 2 minutes on each side. In a mixing bowl, whisk the olive oil, vinegar, shallots, garlic, and basil together. Season the marinade with salt and pepper. Remove the vegetables from the grill. In large, 2-quart ramekin, alternate layering the different vegetables. Pour the marinade over the vegetables and allow to marinate for 12 hours or overnight. Either serve the vegetables in the glass container or on a platter. Garnish with parsley.