Preheat your oven to 375°F and lightly grease a 9×13-inch baking dish. If your chicken breasts are particularly thick, slice them in half lengthwise or gently pound the thicker portions to help them cook evenly. Place the chicken breasts in a single layer in the prepared dish.
In a medium bowl, combine the softened cream cheese, sour cream, garlic powder, onion powder, salt, and black pepper. Stir until smooth and well blended. Spread the mixture evenly over the chicken breasts, making sure each piece is covered.
In a separate bowl, mix the whole berry cranberry sauce, brown sugar, Dijon mustard, and Worcestershire sauce until combined. Spoon the cranberry mixture over the cream cheese layer, spreading it gently to cover the chicken without mixing the two layers.
Sprinkle the shredded mozzarella and cheddar cheese evenly over the cranberry topping. Transfer the baking dish to the oven and bake uncovered for 35-40 minutes, or until the chicken is cooked through and the thickest part reaches an internal temperature of 165°F. Cooking time may vary depending on the thickness of the chicken breasts.
Remove the baking dish from the oven and let the chicken rest for about 5 minutes. This allows the creamy sauce to settle slightly before serving. Garnish with freshly chopped parsley, if desired, and serve warm.