Preheat the oven to 400 degrees F. Generously coat a large rimmed baking sheet with non-stick spray.
If the carrots are thick, cut them in half lengthwise. Cut diagonally into 1 ½-inch thick slices, then place the carrots in the center of the baking sheet. Add the broccoli florets to the baking sheet with the carrots.
In a small bowl, stir together the Italian seasoning, salt, pepper, garlic powder, and onion powder. Drizzle the vegetables with the oil, then sprinkle on the spice mix. Toss to coat the vegetables evenly, then spread them into an even layer.
Place in the oven and roast for 20 minutes, until they are browned and tender, tossing once halfway through. Sprinkle with Parmesan. Enjoy hot.