Start by bringing a large pot of salted water to a boil. Add the cauliflower florets and cook for about 8-10 minutes, or until they are fork-tender. Drain the cauliflower and set it aside.
In the same pot, cook the fettuccine according to the package instructions until al dente. Reserve 1 to 1½ cups of the pasta cooking water, then drain and set the pasta aside.
In a blender or food processor, combine the cooked cauliflower, Parmesan cheese, olive oil, minced garlic, Dijon mustard, butter, lemon juice, sea salt, and freshly ground black pepper. Blend until smooth and creamy. If the sauce is too thick, add a little reserved pasta water until you reach your desired consistency.
In a large skillet over medium heat, add the fettuccine and pour the cauliflower sauce over it. Toss to combine, adding reserved pasta water as needed to help the sauce adhere to the pasta.
Divide the fettuccine Alfredo among plates or bowls. Top with additional grated Parmesan cheese and a sprinkle of chopped fresh parsley for a pop of color. Serve immediately and enjoy your delicious, creamy dish!