In a large saucepan, bring the water to a boil. Add salt to the water, then slowly whisk in the polenta. Cover the saucepan and cook over moderate heat, whisking often, until the polenta is very thick and creamy, about 45 minutes.
Meanwhile, in a small saucepan, cook the butter over moderate heat until starting to brown, about 3 minutes. Add the sage leaves to the saucepan and fry until crisp, about 1 minute. Discard the sage leaves and set the butter aside.
Stir the sage butter and grated cheese into the polenta. Season with salt and pepper and serve hot.
The cooked polenta can stand, covered, for 1 hour. Reheat, whisking vigorously, and stir in the sage butter and cheese before serving.