Preheat outdoor grill or grill pan to medium high. Prepare vinaigrette and set aside. Drain olives. crumble feta, and chop parsley, if using, and set aside.
Wash and dry vegetables. Placing vegetables on a large tray as you go, trim the ends from asparagus and use a vegetable peeler to peel the skin from the bottom third of any larger, woody stems. Trim the ends from the zucchini and cut in half lengthwise. Drain the artichoke hearts, rinse well, cut in half and dry on a paper towel. Remove any wilted leaves from the outside of radicchio and cut into 4 wedges leaving the core intact to hold the wedges together. Peel onion and cut into 8 wedges keeping the root intact. Brush vegetables with olive oil on both sides and season with salt and pepper.
Place on hot grill. The vegetables will take different amounts of time. Asparagus , artichokes and radicchio (5-7 minutes). Zucchini and peppers (6-8 minutes). Onions (up to 10 minutes.). Times will vary depending on your grill and how you like your vegetables cooked. Keep an eye on them. Remove from grill and let cool just enough that you can handle them.
Cut vegetables into large bite sized pieces and place in a large bowl. Add olives and half of the vinaigrette. Toss to coat. Taste and add salt and pepper and more vinaigrette as needed. Serve warm or at room temperature garnished with crumbled feta cheese and chopped parsley. Serve extra vinaigrrette on the side.