Heat the oven to 350 degrees F. Butter a deep (3 Inch) 1-1/2 quart baking or souffle dish (or a deep cast-iron skillet). In a large bowl, whip the egg whites until medium-stiff peaks form; set them aside.

In a mixing bowl, whisk together the cornmeal and 1 cup of the milk. In a medium saucepan, scald the remaining 2 cups of the milk. Add the cornmeal mixture to the saucepan and cook, whisking constantly, over medium-low heat, until the mixture thickens (you'll begin to see the bottom of the pan as you whisk), about 10 minutes. Remove from the heat; stir in the salt, sugar, and butter. Add the egg yolks one at a time, whisking to combine after each addition. Gently fold in the egg whites. Pour the mixture into the prepared baking dish and bake until the spoonbread is puffed, with a golden brown crust, and a toothpick inserted in the center comes out clean, about 1 hour. Serve with lots of butter.