Position racks in the upper and lower thirds of the oven (if using two sheets) or the center of the oven (if using one). Preheat the oven to 400 degrees F. Generously coat two large, rimmed baking sheets with non-stick spray.
Place the vegetables in a great big bowl (or you can toss them right on the two baking sheets, dividing the ingredients between each). Top with the oil and mustard. Sprinkle with Italian seasoning, salt, garlic powder, and black pepper. Toss to coat. Pay special attention to the broccoli florets and make sure they get an adequate amount of oil, as they are more prone to burning.
Divide the vegetables evenly between the two sheets, spreading them into a single layer.
Roast the vegetables at 400 degrees F for 25 to 35 minutes (or if you have the convection option, do a convection bake at 375 degrees F for 20 to 25 minutes). Toss the vegetables, rotate the pans 180 degrees, and switch the pans' positions on the upper and lower racks halfway through. The vegetables should be turning brown and crispy at their edges and tender inside (the cooking time may vary based on your oven). Sprinkle with the Parmesan cheese. Enjoy hot or at room temperature, with additional salt and pepper to taste.
Notes
Adapted from the Italian Roasted Vegetables in my cookbook.
TO STORE: Refrigerate leftovers in an airtight storage container for up to 5 days.
TO REHEAT: Rewarm vegetables on a baking sheet in the oven at 350 degrees F or in the microwave.
TO FREEZE: Freeze leftovers in an airtight freezer-safe storage container for up to 3 months. Reheat from frozen. Once reheated, frozen roasted vegetables may be a bit soggy, but they will still have great flavor.