Bring a large pot of water to a boil over high heat. Add the chicken breasts and return to a boil. Immediately remove the pot from heat, cover with a tight-fitting lid, and allow the chicken to poach for approximately 25 minutes. Once cooked through, transfer the chicken to a plate and let it cool before shredding.
Preheat the oven to 350°F. Lightly grease a 9x9-inch baking dish or similar-sized pan with non-stick spray.
In a medium saucepan over medium-low heat, combine the cubed cream cheese, ranch dressing, hot sauce, black pepper, and garlic powder. Whisk continuously until the cream cheese is fully incorporated into the mixture. Remove from heat.
Stir the shredded chicken, chopped green onions, 1 cup of the mozzarella cheese, and 1 cup of the cheddar cheese into the sauce. Mix thoroughly, then spoon the mixture into the prepared baking dish. Evenly sprinkle the remaining mozzarella and cheddar cheese over the top.
Place in the oven and bake for 20 to 30 minutes, or until the cheese is fully melted and the edges begin to bubble. Switch the oven to BROIL and cook for an additional 2 to 3 minutes, until the top achieves a golden-brown crust. Remove promptly.
Serve hot with tortilla chips, fresh vegetable sticks, or crackers. Leftovers may also be enjoyed wrapped in a tortilla alongside leafy greens.