Preheat the oven to 350 degrees F. Grease a 9 by 13-inch casserole dish.
Slowly bring the half-and-half, 2 tablespoons butter and salt to a boil. Slowly whisk in the grits, stirring constantly for several minutes. Add all the cheeses and allow to melt. Temper the eggs into the grits and stir together. Pour into casserole dish and bake for 25 to 35 minutes. Top with additional grated cheese if desired.