In a large saucepan over high heat, bring the cream and butter to a boil. Reduce the heat to low and simmer for about 1 minute. Add 1/2 of the cheese and whisk until smooth, about 1 minute more. Remove from the heat and season with salt and pepper and a generous pinch of nutmeg. (Be judicious with the salt. Parmigiano-Reggiano is salty, so you don't need much extra salt)
Meanwhile, bring a large pot of water to a boil over high heat. Generously salt the boiling water, add the pasta and cook until al dente (tender but firm to the bite), 1 to 3 minutes, depending on the freshness of the pasta. Drain the pasta well.
Add the pasta to the sauce and use tongs to thoroughly coat the pasta with the sauce. Sprinkle with of the rest of the cheese and toss well. Garnish with fresh parsley.
Serve immediately with extra cheese.