Fill a pot for the pasta with about 6 quarts of water, place over high heat, and bring to a boil.
Cut the butter into 6 to 8 pieces and put it in the bowl you will be serving the pasta in. Add the heavy cream and season generously with salt and
When the water for the pasta is boiling, add about 2 tablespoons salt, add the shells, and stir well. Cook until al dente.
When the pasta is done, drain well, transfer to the bowl, and mix well. Add the grated Parmigiano-Reggiano, mix again vigorously, and serve at once.