In a skillet, cook onion in 1 tbs. putter. Drain onions, reserving dripping in skillet (refrain if onions irritate).
Combine onions, mashed potatoes and egg. Shape into six 3-inch patties. Dip in the flour. (I will sometimes also add the flour into the actual potato mix). Add 3 tbs. butter to skillet. Heat over medium heat. Add potato patties and cook about 5 minutes on each side or until desired brownness.