Peel two large floury potatoes (such as Maris Piper) and cut them into roughly 2.5cm chunks.
Put the potato chunks in a large saucepan and cover with cold water by about 2.5cm. Add 1 teaspoon of salt, bring to the boil, then reduce the heat and simmer for 15–20 minutes, or until the potatoes are easily pierced with a fork.
Drain the potatoes well and return them to the pan over a low heat. Let them steam-dry for 1–2 minutes, then mash until smooth.
Stir in 2 tablespoons of cornflour until a thick dough forms.
Transfer the mixture to a bowl, cover and chill in the fridge for at least 30 minutes.
Lightly flour a clean work surface. Roll out half of the chilled potato mixture to about 6mm thick, then use a 5cm round cutter to cut out circles.
Use a straw to poke two holes for the eyes and the edge of a teaspoon (or a small knife) to carve a smile into each circle. Place the smileys on a baking tray lined with baking paper.
Freeze on the tray for at least 1 hour, or until firm.
Heat about 1 litre of vegetable oil in a deep, heavy-based saucepan to 175°C.
Working in batches, fry a few smileys at a time for 3–5 minutes on each side, or until golden and crisp.
Remove with a slotted spoon and drain on kitchen paper. Season immediately with a little extra salt.
Serve warm with your favourite dips.