Prepare peanut dressing by combining peanut butter, rice vinegar, tamari, sugar (or honey), and ginger in a large mixing bowl; mix well. Whisk in coconut milk until smooth.
Add broccoli slaw, chickpeas, carrots, quinoa, and basil to the bowl; season ingredients with a few pinches of salt. Use tongs to toss well until dressing coats all ingredients. Taste, and season with a pinch more salt, if needed. Serve immediately or refrigerate, covered, for up to 3 days.
