To grill vegetables: Cut the vegetables into larger slices that won’t fall through the grill grates, about ½ inch thick. For the zucchini, it is best to cut it on the diagonal. Cut bell peppers into larger slices. Cut the red onion into rings. Trim the asparagus ends. Toss the vegetables with olive oil, salt, and pepper. Start by grilling the red onions, mushrooms, and bell peppers. They will take 3-5 minutes per side. Then add the asparagus and zucchini. It will take 2-4 minutes per side.
Make the dressing: Add all of the ingredients to a bowl or mason jar. Stir or whisk well to combine. When the vegetables come off the grill, drizzle 2/3 of the dressing over the vegetables. Let rest for 5 minutes. Save the rest of the dressing for serving with the salad.