Prepare the dressing first, so the flavors have a few minutes to blend. In a small bowl or jar, whisk together the oil, vinegar, soy sauce, toasted sesame oil, brown sugar, ginger, and sesame seeds. Set the dressing aside.
Slice the red onion very thinly and soak the slices for a few minutes in ice water to take the edge off. Drain the can of mandarin oranges. Slice the avocado and chop the chicken breast.
To assemble the salads, place about 3 cups of salad greens in each bowl or plate. Top with mandarin orange segments, chopped chicken, sliced avocado, and a few slices of the soaked red onion. Give the dressing one last whisk and then drizzle it over the salads. The dressing is potent, so start with a small amount and add more as needed.
*Use a light flavored or neutral oil, like canola, grapeseed, or an untoasted sesame oil.**This salad works with a variety of salad greens, or even very thinly sliced cabbage.