1. Preheat Your Oven and Prepare Your Dish: Start by preheating your oven to 375 F (190 C). While the oven heats, lightly grease an 8×8 inch baking dish or a similar-sized oven-safe skillet. This prevents the dip from sticking and makes for easier cleanup.

2. Combine Cream Cheese and Sauce: In a large mixing bowl, add the softened cream cheese, buffalo wing sauce, and ranch dressing. Use a spatula or an electric mixer on low speed to beat these ingredients together until they are smooth and well combined. The mixture should be creamy and uniformly orange in color.

3. Stir in Chicken and Cheese: Add the shredded cooked chicken, half of the shredded cheddar cheese (1/2 cup), and half of the shredded mozzarella cheese (1/2 cup) to the cream cheese mixture. Gently fold everything together until the chicken and cheese are evenly distributed throughout the creamy sauce.

4. Transfer to Baking Dish: Spoon the entire chicken mixture into your prepared baking dish, spreading it out evenly with the back of your spoon or spatula. Make sure the surface is relatively flat for even baking.

5. Top with Remaining Cheese: Sprinkle the remaining 1/2 cup of shredded cheddar cheese and 1/2 cup of shredded mozzarella cheese generously over the top of the dip. This layer will melt into a beautiful, golden-brown crust.

6. Bake Until Bubbly and Golden: Place the baking dish in the preheated oven and bake for 20-25 minutes, or until the dip is hot and bubbly around the edges and the cheese on top is melted and lightly golden brown. If you want a more deeply browned top, you can briefly switch to the broiler for the last minute or two, but watch it very carefully to prevent burning.

7. Rest and Garnish: Once baked, carefully remove the dip from the oven. Let it rest for 5-10 minutes before serving. This allows the dip to set slightly and prevents it from being too runny. Garnish with sliced green onions, if desired, for a fresh, savory touch.

8. Serve Warm: Serve the warm, bubbly dip with your favorite dippers like tortilla chips, sturdy crackers, celery sticks, or carrot sticks.