Preheat the oven to 350 degrees F.

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

Over medium heat bring to a boil: milk, salt, cayenne remaining tablespoon of butter. Immediately stir in the grits, and reduce the heat to medium. Whisk steadily while cooking, uncovered, for 6 to 8 minutes, until the grits are tender and creamy. Remove from heat and whisk in 1 1/2 cups cheese until melted. Pour the grits into the prepared pan and sprinkle with remaining cheese. Bake for 20 to 25 minutes, or until the cheese is melted and slightly golden. Serve hot.