Cook pasta according to package instructions. Drain and rinse under cold water to cool. Set aside.
Make the Dressing In a small bowl, whisk together olive oil, vinegar (or lemon juice), Dijon, yogurt, garlic, oregano, salt, and pepper until well blended. Adjust seasoning to taste.
In a large bowl, combine the cooled pasta, chicken, bacon, hard-boiled eggs, cherry tomatoes, mozzarella, and red onion if using.
Pour the dressing over the salad and gently toss until everything is evenly coated.
Stir in the chopped basil. Taste and adjust seasoning with salt and pepper as needed. Serve immediately or refrigerate for 30 minutes to let the flavors develop.