Bring a large pot of water to a boil, add the walnuts, and bring the water back to a boil. Remove saucepan from heat.
Leave nuts in hot water for 10 minutes. Throw them in a colander, let the water drain. Pat the nuts dry with a paper towel, arrange them on a baking sheet and sprinkle with sugar so that it covers the nuts on all sides.
Preheat oven to 120C. Switch off. Place the baking sheet with the nuts in a warm oven for at least 2 hours to dry completely.
Heat the oil, but not very strongly, in a deep fryer or deep pan. Roast the nuts in it in small batches until the sugar has dissolved and the nuts are golden, about 2 minutes. Take them out with a slotted spoon, sprinkle with sesame seeds and leave to dry (but not on paper).