Break eggs into the skillet. Immediately reduce heat to low. Season as desired and cook slowly to preferred firmness, covering with lid, or turn eggs gently to cook both sides. Cover pan tightly to hold in steam. Cook slowly to desired firmness or turn eggs gently to cook both sides, about 4 to 6 minutes.
Gentle heat is the way to perfectly cooked eggs.
Stir gently to break yolk and mix a bit with the white. Season with salt and pepper. When egg is set, turn and cook other side. Place cheese slice on a warmed or toasted hamburger bun. Cook over low heat approximately 1 minute.