Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions until al dente. In the last 3 minutes of cooking, add the broccoli florets to the pot. Drain the pasta and broccoli, reserving 1/2 cup of the pasta water.
In the same pot, heat the olive oil over medium heat. Add the minced garlic and red pepper flakes (if using) and sauté for about 1 minute, until fragrant.
Lower the heat and return the drained pasta and broccoli to the pot. Add the Boursin cheese and a splash of the reserved pasta water. Stir until the cheese melts and coats the pasta and broccoli evenly. If the sauce is too thick, add more reserved pasta water as needed.
Season with salt and pepper to taste. Sprinkle with grated Parmesan cheese and mix well.
Serve immediately, garnished with fresh parsley.