Prepare the potatoes: Peel and slice potatoes into 5 mm rounds. Rinse under cold water and pat completely dry with paper towel.
Make the batter: In a large bowl, whisk together plain flour, cornflour, baking powder, and salt. Gradually whisk in the cold beer or water until smooth and thick — it should coat the back of a spoon without dripping off too quickly.
Heat the oil: Pour oil into a deep frying pan or pot to about 5 cm depth. Heat to 180 °C. (If you don’t have a thermometer, a drop of batter should sizzle and rise immediately.)
Batter and fry: Dip each potato slice into the batter, allowing the excess to drip off. Carefully lower into the hot oil, frying in batches so you don’t overcrowd the pan. Cook for 3–4 minutes per side, or until puffed and golden.
Drain and season: Remove with tongs or a slotted spoon and drain on a wire rack. Sprinkle generously with salt while hot.
Serve: Serve immediately with tomato sauce, malt vinegar, or a squeeze of lemon.