Preheat the oven to 350°F (175°C).
Steam the broccoli florets until tender but still crisp, about 4-5 minutes. Set aside.
In a large skillet, melt the butter over medium heat. Add the chopped onion and minced garlic and sauté until the onion is translucent, about 3-4 minutes.
In a large mixing bowl, combine the cooked rice, shredded chicken, steamed broccoli, sautéed onion and garlic, Knorr Chicken Flavor Rice Sides mix, milk, sour cream, black pepper, and salt. Stir well to combine all ingredients evenly.
Add 1 cup of shredded cheddar cheese and all the mozzarella cheese to the mixture. Stir until the cheese is evenly distributed.
Transfer the mixture to a greased 9×13 inch casserole dish and spread evenly.
Sprinkle the remaining 1/2 cup shredded cheddar cheese evenly over the top of the casserole.
Bake uncovered in the preheated oven for 35-40 minutes, or until the casserole is bubbly and the cheese on top is melted and lightly golden.
Remove from the oven and let it rest for 5 minutes before serving.