Bring a large pot of generously salted water to a rolling boil. Add the fettuccine and cook until al dente according to package directions. Just before draining, reserve 1 cup of the starchy pasta water. Drain the pasta and set aside.
In a large skillet over medium heat, melt the butter. Add the minced garlic and sauté for 1 minute until fragrant but not browned.
Pour in the heavy cream and bring to a gentle simmer. Once small bubbles appear around the edges, reduce the heat to low and let it cook, stirring frequently, for 2–3 minutes until slightly thickened.
Remove the skillet from the heat. Whisk in the freshly grated Parmesan a handful at a time, stirring until completely smooth and melted. Season with salt, black pepper, and a pinch of nutmeg if using. If the sauce is too thick, gradually stir in reserved pasta water, 2 tablespoons at a time, until it reaches a silky, pourable consistency.
Return the skillet to low heat and add the drained fettuccine. Using tongs, toss well to coat every strand in the sauce. Add a little more pasta water if needed to keep the sauce creamy and loose.
Twirl the pasta into warm serving bowls, sprinkle with chopped parsley and extra Parmesan. Serve right away.