Bring a pot of water to a boil and cook pasta according to package instructions.
Heat the oil in a large pot or pan over medium high heat. Add the garlic and red pepper and sauté briefly. Do not let the garlic brown or burn. Turn up the heat to high, and stir in chopped bell peppers and cook for one minute. Add broccoli and sauté until tender, but still crisp and bright green. Season with salt and pepper. Add vegetable mixture to pasta along with cheese.