In a pot, cover potatoes with water and bring to a boil over high heat. Simmer on medium-high heat until the centre of the potatoes are tender when checked with a fork, about 20 minutes. Turn off heat. Drain, return potatoes to pot and allow to completely dry out over remaining heat. Mash until smooth.
Place warm mashed potato in medium bowl. Stir in flour, salt and melted butter. Mix lightly until dough forms.
On a well floured surface, knead the dough lightly. The dough will be sticky. Use a floured rolling pin to flatten into a 22cm circle about 1/2cm thick.
Cut into quarters using a floured knife.
Sprinkle a little flour into the base of a dry frying pan and cook the farls for 3 minutes on each side or until evenly browned. Season with a little salt and serve immediately.