In small bowl prepare the basil dressing or Dijon mustard and mix well. The condiments can be made several hours in advance.
Slice the vegetables into uniform sizes.
Marinate the veggies in a shallow pan for an hour. Drain off the marinade and then grill the vegetables on each side for about 4-5 minutes, until tender yet crisp.
Spread one side of each sandwich slice with your choice of spread. Add the vegetables, next place 1 ounce of cheese and the parsley or lovage. Butter lightly the top and bottom of sandwich. Press down carefully on the sandwich and toast on grilll. Cut in half and serve.