Put the grits in a medium bowl and cover with water. Stir a few times, then let stand for 1 minute. Tilt the bowl slightly, allowing the chaff to float to the top. Spoon off the chaff and drain the grits. Transfer the grits to a large, heavy saucepan. Add the milk and 2 cups of water and bring to a boil, stirring constantly. Cook over low heat, stirring occasionally, until the grains are just barely tender, about 15 minutes. Season with salt and pepper and continue cooking, stirring occasionally, until the grits are tender, about 10 minutes longer.
In a small skillet, melt 1 tablespoon of the butter. Add the corn and cook over high heat until crisp tender, about 2 minutes. Stir the corn into the grits, along with the remaining 2 tablespoons of butter. Serve warm.
The grits can be kept at room temperature for up to 2 hours. Add a few tablespoons of warm water to thin the grits before reheating.