In a large saucepan, combine the water, milk, butter and salt and bring to a boil. Slowly whisk in the stone-ground grits and simmer over low heat, stirring frequently with a wooden spoon, until the grits are very thick, about 1 hour.
Transfer the cooked grits to a large bowl and stir in the cheese. Let cool slightly, then add the egg yolks, 1 at a time, stirring the grits well with a wooden spoon after each addition.
Preheat the oven to 400°. Butter a 2 1/2-quart glass or ceramic soufflé dish. In a large bowl, beat the egg whites until they hold firm peaks. Stir one-third of the beaten egg whites into the grits to loosen them, then fold in the remaining egg whites. Scrape the grits into the prepared soufflé dish and smooth the surface. Bake the soufflé for 30 minutes, or until it is puffed and golden brown and the center is moist but not runny. Serve at once.