1. Place potatoes in a small saucepan; cover with cold water, and bring to a boil over high heat. Cook until very tender, about 12 minutes. Drain; transfer to a medium bowl. Using a potato ricer or a food mill, mash potatoes (you should have 5 cups mashed). Add melted butter, flour, and salt. Stir, using a wooden spoon, until dough comes together. Transfer to a clean work surface; knead until smooth, being careful not to overwork the dough.

2. Heat a griddle over medium heat. Roll out dough to 3/4-inch thickness on a lightly floured surface. Using a 2 1/2-inch cookie cutter, cut out rounds, and prick with a fork. Lightly butter griddle; cook scones in batches until golden brown, about 5 minutes per side. Transfer to a clean kitchen towel, keeping scones covered while cooking remaining scones. Serve warm with butter and jam, if desired.