Add 3 cups water, 1 cup heavy cream, the remaining 2 tablespoons olive oil, remaining 1 3/4 teaspoons kosher salt, and 12 ounces short dried pasta to the Dutch oven, and stir to combine. Bring to a boil over high heat. Continue to boil, stirring occasionally with a wooden spoon to prevent the pasta from sticking to the bottom of the pot, until the pasta is 2 minutes less than al dente, 5 to 9 minutes depending on the pasta shape. Meanwhile, finely grate 1 ounce Parmesan cheese (about 1/2 cup lightly packed) if needed, or measure out 1/3 cup store-bought.
