Combine mixed greens, cucumber, cherry tomatoes, carrot, red onion, and chickpeas (if using) in a large bowl.
In a separate small bowl, whisk together tahini, lemon juice, and water until smooth.
Add minced garlic, salt, and pepper to the dressing and whisk again. Add more water if needed to achieve a pourable consistency.
Drizzle the tahini dressing over the vegetables, starting with about two-thirds and adding more as needed.
Gently toss the salad to coat all ingredients evenly with the dressing.
If using, add feta cheese, avocado, and herbs, giving the salad one final gentle toss.
Sprinkle with toasted sesame seeds just before serving.
Serve immediately, or chill for 15 minutes to allow flavors to develop.