Square off four sides of each potato, then cut into 5mm slices. Stack the slices 2 or 3 a time and cut into thin 5mm sticks. Drop the chips into a large pan of cold water for 30 mins to get rid of excess starch.
Drain in a colander, then tip into a clean tea towel, gather into a bag, twist well and whirl a few times in a large circle to spin out the water (this may be best done outdoors).
Heat a deep-fat fryer, a third full of clean oil, to 180C. Fry the sticks, 2 handfuls at a time, in a chip basket, for about 2 mins until they are a crisp russet brown. Tip onto a paper-lined tray and sprinkle lightly with a little more salt.
If making mussels too (see 'Goes well with') - while the mussels are draining and before you finish the sauce, place the potato sticks in a large shallow bowl, sift over the flour, cayenne and ½ tsp salt; mix well.