Peel and roughly chop the potatoes, then cook in boiling salted water for 8 to 12 minutes, or until tender. Drain, then mash with the butter.
Combine the flour, baking powder and a good pinch of sea salt in a bowl. Add the warm mash to the flour mixture and combine gently with a spoon or your fingers to make a dough.
Gently shape the dough into 2 balls and transfer to a lightly floured work surface. Roll each ball into a circle about 5mm thick, prick all over with a fork, then cut into quarters.
Heat a griddle pan over a medium heat. Once hot, smear with a little butter. Carefully transfer the potato scones, in batches, to the pan and cook for 3 to 4 minutes on each side, or until golden brown.
Serve the hot potato scones with bacon and fried eggs, or scrambled eggs and slices of smoked salmon.