Mix the potatoes, onions, flour, egg, salt, pepper and milk in a medium bowl.
The mixture should be thick enough to cling to a spoon but sag just a bit when you hold a spoonful up in the air.
If it's too thin, add some more flour. Too stiff, add some more milk.
Heat the oil over medium until it just starts to shimmer--about 3 to 5 minutes or so.
Place heaping tablespoons of potatoes in the skillet and spread them with the back of your spoon.
Cook until golden on each side--about 5 minutes per side.
Serve warm or cool to room temperature and refrigerate for later.
Add two tablespoons sour cream to each cup of mashed potatoes for a "loaded" taste and a richer flavor. Taste the potatoes for proper seasoning--this will vary depending on how well seasoned your potatoes were to start with.