To prepare the dressing: In a mason jar with a lid, combine the balsamic vinegar, Dijon Mustard, olive oil and chopped basil. Secure the lid and shake for 1 minute or until the oil and vinegar are combined. Season to taste with salt and pepper.
To prepare the antipasto: Preheat a grill to moderate heat. Slice the zucchini and yellow squash to 1/8-inch thick lengthwise slices. Cut the bell peppers into quarters and remove the seeds. Trim the ends of the asparagus. In a large mixing bowl, combine the zucchini, yellow squash, bell pepper, asparagus, green onions and rapini. Pour half the dressing over the vegetables and toss until combined.
Arrange the vegetables on the grill over medium heat. Cook for 2 minutes on each side until they have a nice char and are just cooked. Remove from the grill and cool to room temperature.
Arrange the vegetables on a large platter. Just prior to serving, drizzle lightly with remaining balsamic dressing and sprinkle with remaining chopped basil.