Preheat the oven to 350 degrees F. Butter a 9-by-12-inch casserole dish. Bring 4 1/2 cups water to a boil in a medium saucepan; add 1 teaspoon salt. Add the grits and cook until thickened, about 5 minutes, whisking constantly.
Add the cheese and 4 tablespoons butter to the hot grits and stir until melted and incorporated. Beat the eggs in a small bowl, then whisk in the milk; slowly stir the egg mixture into the grits. Pour the mixture into the prepared casserole dish. (You can make the casserole to this point up to 1 day ahead; cover and refrigerate.)
Melt the remaining 1 tablespoon butter; pour over the cornflakes in a bowl and stir to distribute the butter. Sprinkle the cornflake crumb mixture on top of the grits. Bake 45 minutes.
Photograph by Anna Williams
Courtesy of Food Network Magazine