Melt half the butter in a large skillet over medium heat. Add half the eggs; cook until lightly set. Place in a lightly greased 13"x9" baking pan.
Melt remaining butter in skillet; cook remaining eggs. Add to eggs already in baking pan. Combine milk and soup; pour over eggs. Top with mushrooms, pepper, onion, and cheese. Regrigerate overnight. Bake, uncovered, at 300° for one hour.