Bring the water and salt to a boil in a large stock pot. While you are waiting for the water to boil, prepare a large bowl of ice water. Add the dry pasta to the boiling water and stir frequently until pasta is tender but not mushy. Reserve ¼ cup of the pasta water, strain and immediately transfer to the ice bath to stop the cooking process. Once pasta has cooled, remove from ice bath and reserve. When you are ready to make the pasta dish, bring another gallon of salted water to a simmer and add the chilled pasta just long enough to reheat it, about 3 minutes, and strain.
In a large mixing bowl, combine the butter, cheese, black pepper, reserved pasta water and hot bucatini pasta. Combine thoroughly until butter is completely melted.
Divide among 6-8 serving bowls.