1. Preheat the oven to 375°F. Spray a deep 1½- to 2-quart baking dish with oil.
2. Bring the milk to a boil in a medium saucepan, preferably nonstick. Gradually pour in the cornmeal with one hand, whisking with the other, creating a very thick mixture. Lower the heat and add the butter and salt. Continue cooking over low heat, stirring almost constantly, for 10 minutes.
3. Remove the cooked mush from the stove and transfer it to a medium-size heat-proof bowl. Let the mush cool to lukewarm, about 20 minutes.
4. Meanwhile, place the egg yolks in a small bowl and the whites in a large, high-sided, non-plastic bowl. When the mush is lukewarm, beat the yolks vigorously with a fork, then mix the yolks into the mush, making sure they are thoroughly and evenly incorporated.
5. Beat the egg whites until stiff and glossy. Gently fold them into the batter as much as you can (the batter will be fairly liquid) and pour this into the prepared dish.
6. Bake until a knife inserted into the center comes out barely clean and the top is deeply golden brown, 40 to 45 minutes. Serve at once, straight from the dish and hot from the oven.