Use electric skillet if possible.
Heat skillet to medium, not too high!
Add butter, heat until melted.
Mix beaten eggs, milk, salt, and pepper.
Pour into heated skillet.
Cook eggs slowly on medium to low heat.
When eggs are slightly firm add Aunt Penney's White Sauce over eggs, mix and cook for about 3 to 5 minutes.
Turn heat to low, add shredded cheese over eggs; cover with lid and let cheese melt, about 5 minutes.