Make the dressing: combine sesame oil, toasted sesame oil, honey, tamari or soy sauce, rice vinegar, grated ginger, grated garlic, orange zest, and sesame seeds in a jar or bowl; whisk or shake until smooth.
Fry the wonton strips: pour enough avocado oil into a skillet to reach about 1/4 inch depth and heat over medium-high until shimmering.
Add the wonton strips in batches and cook 1–2 minutes, stirring, until deeply golden and crisp.
Drain the fried wontons on paper towels and sprinkle with flaky salt.
Assemble the salad: in a large bowl combine shredded cabbage, shredded lettuce, cooked shredded chicken, slivered almonds or peanuts, and orange slices.
Pour about half the dressing over the salad and toss to coat the greens evenly.
Top the salad with sliced avocados, fried wonton strips, and chopped green onions.
Serve with additional dressing and a drizzle of chili oil if desired.