Preheat the oven to 375°F (190°C).
In a large skillet, melt the butter over medium heat.
Add the diced onion and minced garlic to the skillet and sauté for 3-4 minutes until the onion is translucent.
Add the chicken broth, milk, salt, black pepper, and paprika to the skillet. Stir to combine and bring to a simmer.
Stir in the Minute Rice and chopped broccoli florets. Remove from heat, cover, and let it sit for 5 minutes to allow the rice to absorb the liquid.
In a large mixing bowl, combine the cooked chicken, rice and broccoli mixture, and 1 cup of shredded cheddar cheese. Mix well.
Transfer the mixture into a greased 9×13 inch casserole dish.
Sprinkle the remaining 1/2 cup cheddar cheese and 1/2 cup mozzarella cheese evenly over the top.
Bake uncovered in the preheated oven for 20 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let it cool for 5 minutes before serving.