Prepare
Set racks in the upper and lower thirds of the oven and heat the oven to 400°F. Coat two large rimmed baking sheets with cooking spray or a thin layer of olive oil.
Put the bell peppers, zucchini, sweet potato, red onion, and broccoli in a large bowl. Keep the sweet potato pieces smaller than the softer vegetables so everything finishes at about the same time.
Season
Whisk together the olive oil, Dijon mustard, Italian seasoning, salt, garlic powder, and black pepper. Pour it over the vegetables and toss until evenly coated, working a little oil into the broccoli florets.
About 3 min
Roast
Divide the vegetables between the prepared pans and spread them into a single layer without crowding. Roast for 25 to 35 minutes. Halfway through, toss the vegetables, turn the pans, and switch their rack positions.
About 30 min
Finish
Sprinkle the hot vegetables with Parmesan, if using. Taste, add more salt and black pepper if needed, and serve hot or at room temperature.
About 2 min

