Preheat the oven to 350°F (175°C) and lightly grease an 8×8-inch baking dish with cooking spray.
Blend the cottage cheese and Greek yogurt ranch dressing in a food processor or blender until completely smooth.
In a large bowl, mix the shredded chicken, buffalo sauce, blended cottage cheese mixture, black pepper, mozzarella, and ¼ cup cheddar cheese until evenly combined.
Spread the mixture into the prepared baking dish. Sprinkle the remaining ½ cup cheddar cheese evenly on top.
Bake for 25–30 minutes, or until the cheese is melted and the dip is bubbly. Broil for 1–2 minutes at the end if a golden-brown top is desired.
Remove from the oven, sprinkle with chopped green onion, and serve warm with celery, carrot sticks, and tortilla chips.