Bring a large pot of water to boil, add a generous amount of salt, then add the pasta and cook to al dente. Add the broccoli to the pasta water during the last 3 minutes. Drain and set aside.

Meanwhile, heat a large saucepan over medium heat and melt the butter.

Add minced garlic and saute for a minute, then pour in the heavy cream. Stir frequently, until the mixture begins to bubble and simmer. Keep it at a low boil until thickened.

Once the mixture has thickened, remove from the heat and stir in the freshly shredded Parmesan, a little at a time, until it’s fully incorporated and melted.

Add the pasta and broccoli to the sauce and stir to coat completely. Taste and add salt and pepper as desired. Garnish with fresh cracked black pepper and more shredded parmesan, if desired.

Serve immediately.