In a large bowl, combine the cut vegetables with olive oil, mustard, and seasonings, tossing well to ensure even coating.
Spread the vegetables in a single layer across the baking sheets, ensuring they are not overcrowded.
Roast in the preheated oven for 25–35 minutes, tossing and rotating the sheets halfway through, until vegetables are browned and tender. Finish with a sprinkle of Parmesan cheese, if desired.