Bring a large pot of salted water to a boil over high heat. Add the chicken breasts and simmer for 12-15 minutes until cooked through (the internal temperature should reach 165°F). Remove the chicken and let it cool slightly, then shred or chop it into bite-sized pieces. Set aside while you prepare the other components.
Preheat your oven to 350°F. Lightly spray a 9x13 inch baking dish (or similar size) with cooking spray to prevent sticking. This ensures your dip won't stick and will be easy to serve.
In a large pot over medium heat, combine the softened cream cheese, ranch dressing, hot sauce, black pepper, garlic powder, and onion powder. Stir constantly for 3-5 minutes until the cream cheese is fully melted and the mixture is smooth and well combined. The heat should be gentle to prevent scorching—you're creating a creamy base that will coat all your ingredients.
Add the cooked chicken from Step 1 to the sauce base along with 1 cup of the mozzarella cheese, 1 cup of the cheddar cheese, and most of the sliced green onions (reserve some for garnish). Stir well until everything is evenly distributed and coated in the buffalo sauce. Transfer the mixture to your prepared baking dish from Step 2, spreading it into an even layer. Top with the remaining 3/4 cup mozzarella and 3/4 cup cheddar cheese, creating an even layer across the top. I like to mix my cheeses together before topping for more uniform coverage.
Bake in the preheated 350°F oven for 20-30 minutes until the dip is heated through and the edges are bubbly. You'll know it's ready when you see bubbles forming around the edges and the cheese is melted throughout.
Turn your oven to broil on high setting and place the baking dish on the top rack. Broil for 2-3 minutes, watching carefully, until the cheese is golden brown and lightly charred in spots. Remove from the oven and garnish with the reserved sliced green onions. Serve immediately with tortilla chips, crackers, or vegetable crudités. I find that broiling gives the top that irresistible crispy, golden crust that takes this dip from good to restaurant-quality.