How to Make It
In a large skillet, heat the oil until shimmering. Add the diced bread and cook over moderately high heat, stirring, until golden brown, about 4 minutes. Drain the croutons on paper towels.
In a large saucepan, bring the water to a boil. Gradually add the polenta, whisking until smooth. Cook over low heat for 10 minutes, stirring frequently with a wooden spoon. Add the milk and continue cooking, stirring often, until the polenta is tender, about 20 minutes longer. Season with salt and pepper and fold in the croutons and cheese. Spoon the polenta onto plates, drizzle with the melted butter and serve at once.
It is worth making extra polenta just to have leftovers for frying. Spread the polenta on a buttered, rimmed baking sheet, cover and keep in the refrigerator for up to 2 days. Cut the polenta into squares and fry them in a mixture of butter and olive oil until crisp, turning them once with a spatula. Serve immediately.