1. Preheat the oven to 350°. Butter a 13-by-9-inch baking dish. In a large, heavy pot, bring the water to a boil. Sprinkle the grits into the water, stirring constantly, and return to a boil. Cook over low heat, stirring frequently, until the grits are just tender, about 30 minutes. Season generously with salt and pepper and cook, stirring, until the grits are very thick and tender, about 10 minutes longer. Off the heat, stir in the butter and shredded Cheddar cheese, then stir in the beaten eggs.
2. Pour the mixture into the prepared dish and bake for 1 hour, until the grits are bubbling and the top is golden. Let cool for 20 minutes before serving.