In a medium size mixing bowl combine mashed potatoes, egg, flour, salt, garlic, green onions, and chedder cheese. 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. Flip the potato cake over when the bottom is browned (about 10 minutes). Brown the other side (about 10 minutes).