Preheat the oven to 350 degrees F.

Lightly grease a 9 by a 9-inch baking dish or equivalent with 1 tablespoon of the butter.

Heat a saucepan over medium heat and add the milk, salt, cayenne and remaining tablespoon of butter. Bring to a boil, and while stirring, add the grits.

Reduce the heat to medium and continue to stir for about 30 seconds. Turn down to a bare simmer and continue to cook, uncovered, for 6 to 8 minutes, stirring constantly, until the grits are tender and creamy. Remove from heat and one cup of the cheese and stir until melted.

Pour the grits into the prepared pan and sprinkle the remaining cheese. Bake for 20 to 25 minutes, or until the cheese is melted and slightly golden. Serve hot.