Peel the potatoes and cut them into chunks. Place them in a pot of cold, salted water. Bring to a boil and cook until tender, around 15-20 minutes. Drain and let cool slightly.
Mash the potatoes until smooth in a large mixing bowl, ensuring there are no lumps. Allow to cool completely.
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the flour mixture to the mashed potatoes, combining gently until it forms a soft dough.
If the mixture is too dry, add milk or buttermilk a tablespoon at a time until the dough is slightly sticky but manageable.
Turn the dough onto a floured surface and knead gently for a minute until smooth. Divide the dough in half.
Roll each half into a circle about ¼ inch thick. Cut each circle into quarters (you can also use a round cutter for more uniform shapes).
Heat 1-2 tablespoons of butter in a large skillet over medium heat. Fry the farls for about 4-5 minutes on each side, until golden brown and crispy. Add more butter as needed.
Remove from the skillet and place on a paper towel to absorb excess fat.
Serve warm, sprinkled with chopped chives or scallions if desired, and enjoy with butter or alongside your favorite savory dishes!
