Cook pasta according to package instructions. Rinse under cold water and set aside.
Blanch the broccoli in boiling water for 1–2 minutes, then transfer to an ice bath. Drain and chop.
In a small bowl, whisk together mayonnaise, Greek yogurt, lemon juice, Dijon mustard, garlic, salt, and pepper.
In a large bowl, combine cooked chicken, broccoli, pasta, bell pepper, and red onion. Pour dressing over and toss well.
Chill in the refrigerator for at least 1 hour before serving.
Top with chopped parsley and grated Parmesan just before serving.
