Preheat the oven to 375 degrees F (190 degrees C). Prepare a 9x13-inch casserole dish with cooking spray.
Mix cream of chicken soup, Greek-style yogurt, milk, dry onion dip mix, parsley, garlic powder, black pepper, salt, and cayenne pepper in a bowl.
Layer 1 bag potato nuggets into the bottom of the prepared casserole dish; top with broccoli. Pour the chicken soup mixture evenly over the broccoli. Sprinkle Cheddar cheese over the mixture; top with remaining bag potato nuggets.
Bake in preheated oven until hot all the way through, about 1 hour.