In a pot, cover potatoes with water and bring to a boil over high heat. Simmer on medium-high heat until the center of the potatoes are tender when pricked with a fork, about 20 minutes. Turn off heat. Drain, return potatoes to pot and allow to completely dry out over remaining heat. Mash with a potato masher 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 9 inch circle about 1/4 inch thick. Cut into quarters using a floured knife.
Sprinkle a little flour into the base of the skillet and cook the farls for 3 minutes on each side or until evenly browned. Season with a little salt and serve straight away.