Prepare the mixture — In a bowl, mix the mashed potatoes, eggs and the flour, combining until a smooth, somewhat sticky dough forms.
Form the cakes – Take a handful of the mixture and gently press to form into small patties, about ½ inch thick. Continue with the rest of the mixture.
Heat the oil – In a capacious pan, warm a good amount of oil over medium so it shimmers from underneath but not smoke.
Coat if necessary – If the mixture is slightly soft, use a bit more flour to lightly dust the potato cakes to help hold their shape.
Start frying – Gently lower the potato cakes into the hot oil, taking care not to overcrowd the pan.
Fry until golden – Cook for 3–4 minutes per side, or until crispy and golden brown.
Drain excess oil – Transfer the cooked potato cakes onto a paper towel-lined plate to soak up the oil.
Serve and enjoy — Allow to cool slightly before serving, then enjoy on their own or with your favorite dipping sauce!