Whisk 3 tablespoons rice vinegar, 2 tablespoons toasted sesame oil, 1 tablespoon soy sauce, 2 teaspoons honey, and 2 teaspoons minced peeled ginger together in a large bowl. While whisking constantly, slowly pour in ¼ cup of the neutral oil and whisk until incorporated. Taste and season with kosher salt as needed.

Heat the remaining 1 ¾ cups neutral oil in a medium saucepan over medium heat until shimmering. Meanwhile, cut 16 square wonton strips in half, then cut crosswise into ½-inch wide strips. Line a plate with paper towels.

Test the oil by dropping in 1 wonton strip: If it immediately starts bubbling, proceed (if it doesn’t, the oil is not hot enough). Working in 3 batches, fry the wonton strips, stirring constantly, until golden brown and crispy, 45 to 60 seconds. Use a slotted spoon to transfer to the paper towels and sprinkle lightly with kosher salt.

Open 2 (4-ounce) cups mandarin orange slices in juice. Transfer 2 tablespoons of the juice into the dressing and whisk to combine. Drain the remaining orange slices.

Add 6 cups shredded Napa cabbage, 2 cups shredded, cooked chicken, 2 halved and thinly sliced Persian cucumbers, 2 peeled medium carrots cut into matchsticks, ½ of the thinly sliced scallions (about 2 tablespoons), and half of the drained orange slices to the bowl of dressing. Toss to combine. Taste and season with kosher salt as needed.

Garnish with the remaining scallions, remaining orange slices, ⅓ cup coarsely chopped roasted cashews, ¼ cup fresh cilantro leaves if using, and some of the crispy wontons. Serve the remaining wonton strips on the side.