Preheat the oven to 400 degrees F. Cut all vegetables to a similiar shape and size for even roasting. Place the all vegetables onto a jelly roll pan. Add the olive oil and toss to coat. Sprinkle with salt and pepper.
Roast for 25 minutes or until the vegetables are lightly browned, stirring occasionally. Remove the baking sheet from the oven. Pour the sauce over the vegetables and stir to coat. Sprinkle with the oregano.
Roast for 5 minutes more. Sprinkle with the parsley. Serve with the cheese.