Preheat the oven to 350°F (175°C).
Steam the broccoli florets until tender but still crisp, about 4-5 minutes. Drain and set aside.
In a large mixing bowl, combine the Greek yogurt, mayonnaise, Dijon mustard, chicken broth, minced garlic, chopped onion, salt, black pepper, and dried thyme. Mix well until smooth.
Add the shredded cooked chicken and steamed broccoli to the yogurt mixture. Stir gently to combine.
Fold in the shredded cheddar cheese and grated Parmesan cheese.
Transfer the mixture into a greased 9×13 inch casserole dish and spread evenly.
Sprinkle the crushed whole wheat crackers evenly over the top of the casserole.
Bake in the preheated oven for 30-35 minutes, or until the casserole is bubbly and the topping is golden brown.
Remove from oven and let it rest for 5 minutes before serving.