Preheat the oven to 350 degrees F.
Melt 2 tablespoons of the butter.
Combine the melted butter with the panko breadcrumbs and 1 cup of the cheddar, tossing to coat.
In a medium saucepan over medium-low heat, combine the broth, the milk, the bay leaf, and the thyme sprig.
Bring the mixture to a simmer then reduce the heat to low.
Cover the saucepan and keep the mixture warm until ready to use.
In a large, shallow Dutch oven or an ovenproof skillet over medium heat, melt the remaining butter.
Add the onion and the celery to the melted butter and cook, stirring occasionally, until the onion is lightly browned, about 3-5 minutes.
Add the mushrooms, 1/2 teaspoon of the kosher salt, the black pepper, and the red pepper to the Dutch oven.
Cook, stirring occasionally, until the mushrooms are tender, about 3-5 minutes.
Add the garlic to the mushroom mixture and cook until fragrant, about 45 seconds.
Stir the flour into the mushroom mixture until combined. Don't worry if the mixture seems dry.
Remove and discard the bay leaf and the thyme sprig from the broth mixture.
Gradually stir the broth mixture into the mushroom mixture.
Add the remaining cheese into the broth and mushroom mixture and stir until well-blended and smooth.
Stir in the rice, the sour cream, the mayo, and the nutmeg.
Cover the Dutch oven with a tight-fitting lid.
Bake until the rice is tender and the liquid is absorbed, about 25-30 minutes.
Transfer the Dutch over from the oven.
Turn on the broiler.
In a microwave-safe bowl, combine the broccoli, the water, and the remaining salt.
Cover the bowl and microwave until the broccoli is tender and bright green, about 2 minutes on high power.
Drain the broccoli and pat it dry.
Stir the broccoli into the rice mixture in the Dutch oven.
Sprinkle the breadcrumb mixture over the broccoli mixture.
Place the Dutch oven on the middle oven rack and broil until the topping is golden-brown, about 2-3 minutes.
Let the casserole stand for 5 minutes.
Serve.