Step 1: Par-Cook the Rice
Preheat your oven to 375°F (190°C). Grease a 9×13 inch (23x33cm) baking dish. In a medium saucepan, bring 2 ½ cups of the chicken broth to a boil. Stir in the rinsed rice, reduce heat to low, cover, and simmer for 15 minutes. The rice will be just tender but not fully cooked (it will finish in the casserole). Remove from heat and fluff with a fork.

Step 2: Sauté the Aromatic Vegetables
While the rice cooks, melt 3 tablespoons of butter in a large skillet over medium heat. Add the diced onion and celery. Sauté for 6-8 minutes until softened. Add the sliced mushrooms and cook for another 6-7 minutes until they release their moisture and begin to brown. Add the minced garlic, dried thyme, and rosemary; cook for 1 more minute until fragrant. Remove from heat.

Step 3: Create the Luxurious Cream Sauce
In a large Dutch oven or heavy pot, melt 4 tablespoons of butter over medium heat. Whisk in the flour and cook, stirring constantly, for 2-3 minutes to form a light golden roux. Gradually whisk in the warm milk and heavy cream until completely smooth. Whisk in the remaining ½ cup of chicken broth, the cream of mushroom soup, sour cream, Worcestershire sauce, Dijon mustard, and nutmeg (if using). Bring to a gentle simmer and cook for 3-4 minutes until slightly thickened. Remove from heat. The sauce should be rich and coat the back of a spoon thickly.

Step 4: Combine All Components
To the pot with the cream sauce, add the par-cooked rice, sautéed vegetable mixture, and shredded chicken. Season generously with salt and pepper. Gently fold everything together until evenly combined. Fold in 1 cup of the Swiss cheese, 1 cup of the cheddar cheese, and ½ cup of the Parmesan cheese until the cheeses begin to melt into the warm mixture.

Step 5: Assemble the Casserole
Pour the entire mixture into the prepared baking dish, spreading it into a smooth, even layer. In a bowl, combine the remaining Swiss, cheddar, and Parmesan cheeses. Sprinkle this cheese blend evenly over the entire surface of the casserole.

Step 6: Create the Buttery Crumb Topping
In a small bowl, mix the Panko breadcrumbs, melted butter, chopped parsley, and paprika until the crumbs are evenly moistened. Sprinkle this mixture evenly over the cheese layer.

Step 7: Bake to Golden, Bubbling Perfection
Place the baking dish on a rimmed baking sheet (to catch any bubble-overs). Bake, uncovered, for 35-45 minutes, or until the topping is deep golden brown, the cheese is bubbly, and the casserole is heated through and jiggles only slightly in the center.

Step 8: Rest, Garnish, and Serve
Remove from the oven and let the casserole rest for 15-20 minutes. This rest is non-negotiable—it allows the sauce to thicken and set, transforming it from soupy to perfectly creamy and sliceable. Garnish generously with sliced green onions and fresh parsley before serving.