Bring a large pot of water to a boil, and salt generously. Add the pasta, and boil according to package directions until al dente, tender but still slightly firm. Strain, and toss with a splash of oil.
Meanwhile, arrange the shrimp in a single layer on a large pie pan or paper plate, and pat them with a paper towel until completely dry. Season with salt and pepper.
Heat a large skillet over medium heat, and add 2 tablespoons of the butter. When the butter melts, raise the heat to medium-high, and invert the plate of shrimp over the skillet so the shrimp fall into the pan all at once. Cook the shrimp, without moving them, until the underside is pink, 1 to 2 minutes. Flip the shrimp, and cook until fully pink and cooked through, about 2 minutes more. Transfer the shrimp to a bowl.
Reduce the heat to medium, and add the remaining 6 tablespoons butter. Scrape the bottom of the skillet with a wooden spoon to release any browned bits. When the butter has mostly melted, whisk in the cream and nutmeg and bring to a simmer, then cook for 2 minutes. Lower the heat to keep the sauce warm.
Whisk the Parmigiano-Reggiano into the sauce. Add the shrimp and cooked pasta, and toss well. Season with salt and pepper. Serve hot in heated bowls.
Don't worry if it seems like there is too much sauce. As soon as everything is tossed together, the sauce will start to cling to the pasta and thicken before your eyes.
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