Melt butter in saucepan and stir in flour, pepper and milk. Cook on medium heat, stirring until thickened.
Add cheese and stir until melted.
Add cooked sausage and half of the cheese sauce to the cooked grits.
Grease a 2-quart casserole dish. Pour in the grits mixture. Make four indentations in the grits with the back of a large spoon. Break one egg into each indentation.
Bake for about 20 minutes or until eggs are cooked through.
