How to Make It
In a large saucepan, cover the walnuts with water. Simmer over moderately low heat until soft, about 50 minutes; drain. Spread the nuts on a rack to dry.
In a medium saucepan, combine the sugar with the 1/2 cup of water. Bring to a boil and simmer over moderately high heat until the syrup reaches 230° on a candy thermometer, about 15 minutes. Add the walnuts and stir to coat them completely. Transfer the walnuts to a baking sheet in an even layer and let cool.
In a large saucepan, heat the oil until it reaches 350°. Fry the walnuts in 4 batches: for each batch, carefully lower the nuts into the hot oil and when it bubbles up, stir well. Fry the nuts until shiny and crisp, about 4 minutes. With a slotted spoon, transfer the nuts to a rack set over a baking sheet and sprinkle with some of the sesame seeds. Repeat with the remaining walnuts, reducing the heat if the oil gets too hot.