Make the miso-sesame dressing: combine white miso, toasted sesame oil, grated ginger, rice vinegar, ponzu, and lemon or lime juice in a blender or food processor and blend until smooth.
Stir in the toasted sesame seeds and season the dressing with salt and chili flakes to taste.
Prepare the bowls: divide baby arugula, shredded cabbage, sliced Persian cucumbers, and halved cherry tomatoes among bowls.
Toss the greens and vegetables with enough miso dressing to lightly coat them.
Add cooked white rice and shredded rotisserie chicken to each bowl.
Top with sliced avocado and chopped cilantro or basil, and drizzle additional dressing over each bowl if desired.
Serve with wonton chips on top or alongside for crunch.