Pre-heat the oven to 350 degrees. Melt ½ cup butter in a large saucepan over low heat. Mix in flour, salt, and pepper. Stir until well blended.
Cook while stirring for about 1 minute.
Remove from heat and gradually stir in milk. Return to heat and cook until thickened and bubbly.
Stir in ham, green pepper, onion, and ½ cup cheddar cheese. Stir gently until mixed well.
Add potatoes into a good grease 13×4″ baking dish.
Pour milk/ham mixture over sliced potatoes and gently mix. Cover with aluminum foil.
Bake at 350 degrees for 30 minutes. After 30 minutes remove aluminum foil and continue baking for 1 hour.
During the last few minutes of cooking top with additional shredded cheddar cheese (optional).