Bring the water and salt to a boil in a large saucepan. Reduce the heat to moderately low so that the water comes to a simmer.
Begin pouring in the polenta taragna by the handful, in a thin stream, very slowly, and stir constantly with a long handled wooden spoon to avoid lumps. Keep the mixture at a bare simmer and stir frequently. (It is not necessary to stir constantly if the polenta is cooked on low heat.) After all the polenta is added, stir in 3 tablespoons of the butter and cook the polenta for 20 to 25 minutes. As it cooks, the polenta will thicken considerable; just keep stirring, and crush against the side of the pan any lumps that might form. The polenta is done when it comes away effortlessly from the sides of the pan.
Remove the pan from the heat and stir in half of the cheese, the remaining 3 tablespoons butter, and pepper. Season to taste. Add remaining cheese and stir quickly, leaving some of the cheese unmelted. Transfer the polenta to a serving platter and serve immediately.