If you're starting with raw chicken, bring a large pot of water to a boil, add the chicken breasts, and let them poach for about 25 minutes with the heat off and the lid on. Once they're cool enough to handle, shred them with two forks. This step takes the longest, so I often do it a day ahead to save time later.
While the chicken cooks or rests, preheat your oven to 350°F and spray a 9x9-inch baking dish with non-stick cooking spray. Having this ready means you can move straight from stovetop to oven without any scrambling once your sauce is done.
In a medium saucepot over medium-low heat, combine the cubed cream cheese, ranch dressing, hot sauce, black pepper, and garlic powder. Whisk constantly until the cream cheese fully melts into the sauce and everything looks smooth and creamy.
Remove the sauce from the heat and stir in the shredded chicken, chopped green onion, and one cup each of the mozzarella and cheddar cheese. Mix well so every bit of chicken gets coated in that spicy, creamy sauce.
Transfer the mixture into your prepared baking dish and top with the remaining cheese. Bake for 20-30 minutes, then switch to broil for 2-3 minutes to get that gorgeous golden top. Watch it closely during broiling so it doesn't burn.
Pull the dip out once it's bubbling and lightly browned on top. Let it sit for a couple of minutes before serving so it firms up just slightly and is easier to scoop.