Preheat your oven to 350°F (175°C). Lightly grease an 8x8 inch or 9x9 inch square baking dish.

Place the fully softened 8-ounce block of cream cheese into a large mixing bowl. Beat the cream cheese with an electric mixer or wooden spoon until it is completely smooth and creamy.

Pour the 1/2 cup of buffalo wing sauce and the 1/2 cup of ranch or blue cheese dressing into the bowl. Stir or beat the mixture until the sauces are thoroughly combined and the base is a uniform orange color and smooth texture.

Fold in the 2 cups of shredded cooked chicken. Add 1 cup of the shredded cheddar or Monterey Jack cheese to the mixture. Reserve the remaining 1/2 cup of cheese for the topping. Stir all ingredients gently until the chicken and cheese are evenly coated in the creamy sauce.

Spoon the entire mixture evenly into the prepared baking dish. Spread the dip level with the back of a spoon. Sprinkle the reserved 1/2 cup of shredded cheese evenly over the top.

Bake the dip for 20 to 25 minutes, or until the dip is hot throughout, the edges are bubbly, and the cheese topping is fully melted and lightly golden brown.

Carefully remove the dip from the oven. Let it rest for 5 to 10 minutes before serving. If desired, sprinkle the optional chopped green onions or blue cheese crumbles over the top before serving hot with celery sticks, carrots, tortilla chips, or slices of baguette.