Cook pasta according to package directions, reducing cooking time by 1 minute for firmer texture. Drain thoroughly and rinse under cold water to stop cooking. Toss with 1 teaspoon of olive oil to prevent sticking.
In a medium bowl, whisk together Greek yogurt, remaining olive oil, lemon juice, Dijon mustard, and minced garlic until smooth and creamy. Season with salt and pepper to taste.
In a large serving bowl, combine the cooled pasta, diced chicken (or chickpeas), cherry tomatoes, cucumber, red onion, Kalamata olives, parsley, and basil.
Pour the Greek yogurt dressing over the mixture and toss gently until everything is evenly coated.
Fold in most of the crumbled feta cheese, reserving a small amount for garnish.
Refrigerate the pasta salad for at least 30 minutes before serving for best flavor absorption.
Just before serving, give the salad a quick toss and top with the reserved feta cheese and additional fresh herbs if desired.