01 - Place potatoes in a pot of cold salted water. Bring to a boil and simmer for 12–15 minutes until fork-tender. Drain well and return to pot to steam dry for 1–2 minutes.
02 - Mash potatoes until smooth. Add butter and milk; mash together until creamy. Allow to cool for 5 minutes.
03 - Stir in scallions, flour, salt, and pepper. Mix to form a soft, non-sticky dough; add more flour if needed.
04 - Lightly flour work surface. Turn out dough and gently knead until smooth. Flatten to 1/2 inch thick. Cut into rounds using a 3-inch cutter or shape by hand into patties.
05 - Heat large nonstick skillet over medium heat and add butter. Fry potato cakes in batches, 3–4 minutes per side, until golden brown and crisp.
06 - Serve warm, with extra butter if desired.