In a heavy medium saucepan, bring the water to a boil over high heat. Stir the polenta and salt into the water, lower the heat to medium-low and simmer, covered, stirring from time to time. Cook until the polenta is cooked through and thickens, about 20 to 25 minutes.
Remove the pan from the heat and stir in the butter until smooth. Pour the polenta onto a lightly oiled, baking sheet and spread to about 3/4-inch thick. Cover tightly with plastic wrap and refrigerate until firm, at least 4 hours and up to 1 day in advance.
Run a knife around the edge of the baking sheet and unmold the polenta onto a cutting board. Cut into 1 1/2-inch squares and refrigerate, wrapped, until ready to cook.
In a large skillet, heat 2 tablespoons of the oil over medium-high heat. Add the polenta squares in batches and cook quickly until golden brown on both sides, about 5 minutes. Remove from the pan and repeat with the remaining polenta, adding more oil as needed.
Yield: 4 servings