Place racks in upper and lower thirds of the oven and preheat oven to 400 degrees F.
Scrub the sweet potato and cut into 1/2-inch cubes and the cauliflower into florets. Place them on the first sheet pan and drizzle with 1 1/2 tablespoons oil.
Cut the zucchini into 1/2-inch cubes and the red onion into 1/2-inch slices. Place on the second sheet pan and drizzle with 1 1/2 tablespoons oil.
Sprinkle each sheet pan with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Toss to coat, then spread the vegetables into an even layer. Place in oven and roast for 10 minutes. Remove the pans from the oven, then with a spatula toss the vegetables to promote even cooking. Spread back into an even layer, rotate the pans' positions, then continue baking until the vegetables are crisp-tender about 10 to 15 additional minutes.
While the vegetables roast, prepare the dressing: in a small bowl or large liquid measuring cup, whisk together the dressing ingredients: olive oil, vinegar, garlic, oregano, mustard, salt, and pepper.
Once the vegetables have finished roasting, scrape them into a large serving bowl. Add the chickpeas. While the vegetables are still warm, pour the dressing over the top and toss gently to coat.
Gently stir in the feta and parsley. Enjoy with pita, couscous, or quinoa as desired.
TO STORE. Refrigerate roasted vegetables in an airtight storage container for up to 5 days.