Put mozzarella cheese in a microwave-safe bowl. Microwave one minute. Stir. Microwave 30 seconds. Stir. At this point, all the cheese should be melted. Microwave 30 more seconds until uniform and gloopy (it should look like cheese fondue at this point). Mix in the butter until it melts and then add the egg, flour, and baking powder. You will need to dump it onto wax paper and knead it by hand to thoroughly incorporate the ingredients or you can do this in a food processor with the dough blade.
Press or roll into a large rectangle on a parchment lined baking sheet using wet hands. Mix together the cream cheese, butter, garlic powder, and mustard in a medium bowl until well combined. Stir in the chicken, ham, and cheese. Place spoonfuls down the center of the rectangle. Roll into a log.