Preheat your oven to 425°F. Lightly spray two rimmed baking sheets with nonstick spray to prevent the vegetables from sticking.
In a large bowl, toss together the broccoli florets, cauliflower florets, baby carrots, and thinly sliced red onion. Add the olive oil, 1/3 cup grated Parmesan cheese, minced garlic, garlic salt, dried thyme, dried rosemary, and freshly ground black pepper. Mix well until all the vegetables are evenly coated with the seasonings. I always make sure the oil is distributed well so every bite is flavorful.
Spread the seasoned vegetables into a single layer on the prepared baking sheets. Roast them in the preheated oven for 20 minutes, then stir them gently to ensure even browning. Return to the oven and continue roasting for another 20 minutes, or until the vegetables are golden brown and caramelized.
Remove the baking sheets from the oven. Sprinkle the freshly grated Parmesan cheese over the hot, roasted vegetables and garnish with chopped fresh parsley before serving. For a bolder finish, I like to add a touch more black pepper right at the end.