In a skillet over medium-high heat, lightly cook the chopped prosciutto until it becomes nice and crispy. Drain any excess fat and allow it to cool completely.
In a large mixing bowl, combine the softened cream cheese, sour cream, Parmesan, mozzarella, dried dill, thyme, onion powder, and garlic powder. Mix everything thoroughly until the mixture is smooth and well combined.
Gently fold in the cooled crispy prosciutto, chopped salami, olives, and roasted red peppers until they are evenly distributed throughout the creamy cheese mixture.
Slightly moisten your hands, then roll the mixture into small, bite-sized cheese balls.
In a separate shallow bowl or plate, mix together the chopped walnuts and pistachios. Roll each cheese ball in this nut mixture, pressing gently to ensure a good coating.
Place the prepared cheese balls in the refrigerator to chill for at least 1 hour before serving to help them firm up.