Cover potato chips with cold salted water in a saucepan and bring to the simmer over medium-high heat until just tender (7-8 minutes). Drain, then spread on a tray lined with several layers of absorbent paper and set aside to dry (2-3 hours).
Meanwhile, preheat oven to 180C. Wrap garlic loosely in foil and roast until golden and tender (15-20 minutes). Squeeze from skins into a bowl, add olive oil and set aside.
Heat cottonseed oil in a large saucepan to 140C. Fry chips in batches until pale golden (7-8 minutes; take care, hot oil may spit), drain on absorbent paper and set aside, then increase oil temperature to 180C.
Meanwhile, combine sea salt and rigani in a bowl and set aside.
Deep-fry chips again in batches until crisp and dark golden (2-3 minutes; take care, hot oil may spit), then drain on absorbent paper. Toss in garlic oil and serve hot with feta crumbled over, and seasoned to taste with rigani salt.