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
Recipe courtesy of Trisha Yearwood for Food Network Magazine