In a medium size mixing bowl combine mashed potatoes, egg, flour, salt (if needed) and garlic salt. Mix well.

Melt butter in a large frying pan over a low heat. Drop pancake-size (4 inch circles) lumps of mashed potatoes into the frying pan. Pat to flatten to 1/2 to 1 inch thickness. Sprinkle some cheddar cheese onto the mashed potato cake. Spoon more potato mixture over the cheese. Flip the potato cake over when the bottom is browned (about 10 minutes). Brown the other side (about 10 minutes).