Bring a large pot of water to a boil. Add the fettuccine and cook for 5–8 minutes. Reserve ½ cup of the pasta water and then drain the fettuccine.
While the pasta cooks, melt the butter in a large skillet over MEDIUM heat. Sauté the garlic for 2 minutes.
Add the flour. As you do so, continue to whisk to make a paste. Slowly pour in the milk, continuing to whisk to remove any lumps. Simmer for 5 minutes to thicken the sauce. Add the broccoli florets and Parmesan. Add the pasta water in increments until the desired consistency is achieved. Stir occasionally with a wooden spoon for another 8–10 minutes.
Add the pasta. Toss to coat everything in the creamy sauce.