In a heavy skillet, brown sausage, breaking up with spatula.
Drain off excess fat; set aside.
In a saucepan, bring salted water to a boil and stir in grits.
Cover, reduce heat to low, and continue cooking for 5 minutes longer, stirring occasionally.
In a medium saucepan, melt butter; stir in flour, pepper and milk.
Cook, stirring constantly, until thickened. Add cheese, stirring until blended.
Add sausage and half of the cheese sauce to cooked grits.
Pour mixture into lightly greased casserole. With back of a large serving spoon, make 4 indentations in grits.
Break an egg into each indentation.
Bake at 325° for 15 to 18 minutes, or until eggs are done as desired.
Reheat remaining cheese sauce to serve with grits and eggs.
