Bring a large pot of salted water to a boil over high heat. Add the pasta and cook, stirring occasionally. After 5 minutes, add the broccoli florets to the pasta and stir and cook for another 4 minutes. Drain pasta and broccoli, reserving 1 cup of the pasta water.

Meanwhile, in a large skillet, heat the olive oil and butter over medium heat. Add the garlic, and red pepper flakes (if used) and cook for 5 minutes. Add the broccoli, pasta, salt and pepper and toss. Add some of the reserved pasta water, if necessary, to make a light sauce. Transfer to a serving platter and sprinkle with Parmesan and parsley.