Cook the Rice: In a saucepan, combine the rice and chicken broth. Bring to a boil, then reduce heat to low, cover, and simmer for 18-20 minutes, or until the rice is cooked and the liquid is absorbed. Fluff with a fork and set aside.

Prepare the Broccoli: Steam or blanch the broccoli florets for 3-5 minutes, until slightly tender-crisp. Drain well and set aside.

Sauté the Aromatics: In a large skillet or Dutch oven, melt the butter over medium heat. Add the onion and cook until softened, about 5 minutes. Add the garlic and cook for another minute, until fragrant.

Make the Cream Sauce: Whisk in the flour and cook for 1-2 minutes, stirring constantly, to create a roux. Gradually whisk in the milk, making sure to smooth out any lumps. Bring to a simmer, stirring occasionally, and cook until the sauce has thickened, about 5-7 minutes.

Season the Sauce: Stir in the salt, pepper, and nutmeg (if using).

Assemble the Casserole: Remove the skillet from the heat. Stir in the cooked rice, shredded chicken, broccoli florets, cheddar cheese, and Monterey Jack cheese. Mix well to combine.

Transfer to Baking Dish: Pour the mixture into a greased 9x13 inch baking dish.

Add Topping (Optional): In a small bowl, combine the breadcrumbs and melted butter. Sprinkle over the casserole. Sprinkle the grated Parmesan cheese evenly over the top.

Bake: Bake in a preheated oven at 350°F (175°C) for 20-25 minutes, or until the casserole is heated through and the cheese is melted and bubbly.

Rest: Let the casserole rest for 5-10 minutes before serving. This allows the sauce to thicken slightly and the flavors to meld.