Reserve some pasta water, then drain the pasta. Return pasta to the pot along with the sour cream, Dijon mustard, salt, pasta water, Parmesan, and black pepper. Stir in the shredded chicken and mozzarella.
Transfer the mixture to the baking sheet with the kale and tomatoes. Toss to combine and spread on a baking sheet. Top with the panko mixture and mozzarella. Roast the pasta.