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.