For sauce, melt butter in a saucepan, then blend in flour. Cook over moderate heat and slowly stir in milk. Season with salt & pepper and continue cooking until sauce is smooth and boiling.
Reduce heat and add cheese, stirring, until cheese is blended, then add green pepper/pimento mixture, stir, and remove from heat.
Grease a baking dish and fill with alternate layers of potatoes and sauce.
Bake in moderate oven, 350 degrees, until potatoes are done, about 1 to 1-1/2 hours. Potatoes may be turned with a spoon to ensure even cooking.