Peel the potatoes and cut lengthways into roughly 1cm/½in slices. Cut each slice into fairly thick chips and rinse in a colander under plenty of cold water to remove excess starch. (If you have time, it's worth letting the chips soak in a bowl of cold water for several hours, or overnight.) Pat dry with kitchen paper.
Heat a deep, heavy-bottomed saucepan half-full of the sunflower oil to 130C. It's important to use a cooking thermometer and check the temperature regularly. Alternatively, use an electric deep-fat fryer heated to 130C. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Using a large, metal, slotted spoon, gently lower half the chips into the hot oil and stir carefully. Fry for ten minutes, or until cooked through but not browned.
Remove the chips from the pan with a slotted spoon and set aside to drain on plenty of kitchen paper. Repeat the process with the remaining chips. (The chips can be left for several hours at this stage.)
When ready to serve, reheat the oil to 190C. With a slotted spoon, lower all the par-cooked chips gently into the pan and cook for 4-5 minutes, or until crisp and golden-brown. Remove from the pan with a slotted spoon and drain on kitchen paper.
Tip into a serving dish and sprinkle with salt and vinegar to serve.