Chop the romaine lettuce and add it to a large bowl. Thinly slice the cabbage (I prefer using a mandolin) and add to the bowl.
Cut the cucumber into small pieces then transfer onto a couple paper towels. Let the cucumbers sit here for about 10 minutes to let some of the water release.
Meanwhile, cut the chicken into small pieces. Finely chop the cilantro and green onions. Chop the peanuts into smaller pieces. Add everything to the large bowl.
To make the dressing, add all the ingredients to a jar: olive oil, sesame oil, rice vinegar, honey, soy sauce, grated garlic, grated ginger, and sesame seeds. Put a lid on the jar and shake until the dressing is fully combined.
To assemble, squeeze any remaining water from the cucumbers, then add to the large bowl. Add as much dressing as you want and toss until everything is well coated and combined.
Divide into bowls and top with avocado and extra sesame seeds (optional).