Heat the oven to 375°F and grease a 2 1/2-quart baking dish.
Combine the rice, rotisserie chicken, tomatoes, broth, salt and black pepper in the dish.
Cover with foil and bake until the center is hot and the tomatoes soften, 18 to 20 minutes.
Remove the foil, scatter the mozzarella over the rice and bake until melted, about 5 minutes.
Dollop the pesto over the casserole and fold it through in broad streaks rather than mixing it completely.
Finish with Parmesan and serve while the cheese is still soft.