In a large bowl, combine the broccoli and cauliflower florets. In a separate small bowl, whisk together the olive oil, salt, black pepper and red pepper flakes. Pour the mixture over the broccoli and cauliflower and toss to coat the vegetables.
Place seasoned florets on a greased or parchment lined baking sheet. Roast for about 15 to 20 minutes or until slightly tender and lightly browned.
Toss the vegetable mixture with balsamic vinegar and Parmesan cheese and serve immediately.