Cook and shred the chicken. Season with salt, pepper, and garlic powder before cooking for best flavor. Set aside to cool.
Blanch broccoli florets in boiling water for 2 minutes, then immediately transfer to an ice bath to stop cooking. Drain thoroughly and chop into bite-sized pieces.
In a large bowl, combine the shredded chicken, blanched broccoli, diced celery, finely chopped red onion, and dried cranberries if using.
In a separate medium bowl, whisk together the mayonnaise, Greek yogurt, lemon juice, salt, and pepper until smooth. If using, add honey and Dijon mustard.
Pour the dressing over the salad ingredients and gently toss until everything is evenly coated.
If using cheese and almonds, fold them in gently after the dressing has been incorporated.
Cover and refrigerate for at least 20 minutes before serving to allow flavors to meld together.