Prepare the chicken. Preheat the oven to 375°F and lightly grease a 9x13-inch baking dish. If the chicken breasts are very thick, slice them in half lengthwise or gently pound them so they cook more evenly. Arrange the chicken in the baking dish.
Make the cream cheese layer. In a bowl, mix the softened cream cheese, sour cream, garlic powder, onion powder, salt, and black pepper until smooth and creamy. Spread the mixture evenly over the chicken.
Add the cranberry sauce. In a small bowl, stir together the cranberry sauce, brown sugar, Dijon mustard, and Worcestershire sauce. Spoon the cranberry mixture over the cream cheese layer.
Add the cheese and bake. Sprinkle the mozzarella and cheddar evenly over the top. Bake uncovered for about 35–40 minutes, or until the chicken reaches an internal temperature of 165°F.
Rest and serve. Let the chicken rest for about 5 minutes before serving. Sprinkle with fresh parsley if you like.