Finely grate the Parmesan (it should be fluffy and powdery for easy melting) and cut the cold butter into small cubes; keep the butter chilled.
In a medium saucepan, combine the heavy cream, minced garlic, lemon zest, and nutmeg. Set over medium-low heat and warm gently, stirring occasionally, until the edges just begin to show tiny bubbles, 3 to 4 minutes (do not brown the garlic).
Raise heat to medium and let the cream reduce slightly to concentrate, 5 to 6 minutes, stirring now and then until it lightly thickens.
Take the pan off the heat and wait 30 seconds. Whisk in half of the Parmesan in small handfuls until smooth, then add the remaining cheese gradually, whisking constantly to avoid clumping.
Return the pot to low heat and whisk in the cold butter, a few cubes at a time, until the sauce looks glossy and slightly thicker, 1 to 2 minutes.
Season with kosher salt and black pepper to taste. If the sauce seems too thick, loosen with a spoonful of hot water from your pasta pot and whisk until silky.
Let the sauce rest off heat for 1 minute to set, then toss immediately with hot pasta or spoon over cooked chicken or shrimp. Serve right away.