Fill a large stockpot with 4 quarts (4 L) of water, stir in 1 tablespoon of kosher salt, cover, and set over high heat. Grate the Parmigiano-Reggiano, mince the garlic, chop the parsley, and measure the cream.
When the water boils, add the fettuccine and stir for the first 30 seconds. Cook for 1 minute less than the package directions, usually 9 to 11 minutes.
Set a medium saucepan over medium-low heat and melt the unsalted butter completely, 1 to 2 minutes, swirling the pan once or twice. Keep it from browning.
Add the minced garlic and stir constantly for 30 to 60 seconds, just until fragrant. Do not let the garlic take on color.
Pour in the heavy cream slowly while whisking, then raise the heat to medium. When small bubbles appear at the edge, lower the heat to low and simmer gently for 5 minutes, whisking often, until the cream thickens slightly.
With the heat on low, add the grated cheese a small handful at a time, whisking until each addition melts. Stir in the black pepper and optional nutmeg, then taste and add salt only if needed. Turn off the heat and cover.
About 1 minute before the pasta is done, scoop 1/2 cup (120 ml) of the starchy pasta water into a heatproof measuring cup. Drain the fettuccine in a colander without rinsing.
Return the drained fettuccine to the empty stockpot off the heat and pour the sauce over it. Toss with tongs for about 1 minute, adding reserved pasta water 1 tablespoon at a time until the sauce turns glossy and loose.
Divide the pasta among four warmed bowls. Sprinkle each with chopped parsley, extra grated Parmesan, and a few turns of black pepper, then serve right away.