Start by boiling water in a big pot and tossing in the fettuccine. As it cooks, you will notice the aroma of pasta filling the air. This usually takes about ten minutes. Be careful not to overdo it; you want it al dente, not mushy.
While the pasta cooks, steam the broccoli florets until they are bright green and tender. This usually takes around five to seven minutes. Avoid boiling it too long; you do not want to lose that vibrant color.
In a separate pan, melt the butter over medium heat. Once it is bubbly and fragrant, whisk in the flour until it is mixed well and starts to brown a bit. The light nutty aroma will tell you it is time to add the milk, which helps create that rich sauce. Do not rush this step; the flour needs time to toast.
Slowly whisk in the milk, making sure to stir continuously. You will notice it thickening as you go, and it should become creamy without lumps. It is important to add the milk gradually; dumping it all at once can lead to a clumpy sauce.
Once the sauce thickens, stir in the grated parmesan and sprinkle in the nutmeg, salt, and pepper. It should smell cheesy and a bit nutty now. Make sure to taste and adjust the seasoning as you like, but be careful with the salt—it is easy to go overboard.
Drain the cooked fettuccine and gently toss it with the broccoli in the sauce. You want everything coated evenly, and the aroma will be mouthwatering. Take your time to mix, but avoid over-stirring, as you do not want to break the pasta or broccoli.
Finally, ladle the broccoli fettuccine Alfredo into bowls, and maybe add a little extra parmesan on top if you fancy. The smell should be inviting, making it hard to resist. Keep a watchful eye on the pasta; it is best served right away while the sauce is nice and creamy.