Melt the butter and cook the garlic. In a large saucepan or deep skillet over medium heat, melt the butter. Add the minced garlic and cook for about 1 minute, stirring constantly, until fragrant and just barely golden. Don't let it brown — burnt garlic turns bitter.
Add the cream and simmer. Pour in the heavy cream and stir to combine. Bring to a gentle simmer (small bubbles around the edges, not a rolling boil), then reduce heat to medium-low. Simmer 3–4 minutes, stirring occasionally, until slightly thickened.
Whisk in the Parmesan. Remove the pan from the heat — this is the most important step. Add the freshly grated Parmesan a handful at a time, whisking constantly until each addition melts before adding the next. Adding it off the heat keeps the cheese smooth instead of clumpy.
Season and finish. Stir in the salt, pepper, and nutmeg (if using). Taste and adjust.
Toss and serve immediately. Add hot, drained fettuccine right into the pan and toss until every strand is coated. If the sauce feels too thick, loosen it with a splash of warm pasta water. Serve right away with extra Parmesan and chopped parsley.