Melt 2 tablespoons of the butter with the olive oil in a deep skillet or stockpot over medium heat. Add the celery and onion then cook until the vegetables start to soften, about 5 to 7 minutes.
Stir in the mushrooms and cook for an additional 8 to 10 minutes, allowing the mushrooms to release their liquid and brown slightly. Season with 1 teaspoon of the kosher salt and ¼ teaspoon of the black pepper.
Melt the remaining butter then toss in the flour, stirring to blend into the vegetables. Cook for about 3 minutes. Stir in the chicken stock.
Add the broccoli, thyme and parsley, cook for about 10 minutes or until it’s just tender.
Stir in the rice, cover and reduce the heat to medium-low. Cook for 20 minutes, stirring about every 10 minutes.
Pour in the milk and continue cooking for another 15 to 20, or until the rice is tender, stirring occasionally. Check for seasoning, adding the remaining kosher salt and pepper if needed.
Turn off the heat and stir in the mayonnaise, sour cream and the nutmeg along with 1 cup of the shredded cheese. Transfer to a large baking dish that has been sprayed with cooking spray and top with the remaining cheese.
Cover the dish with foil and bake in a 350-degree oven for 20 minutes then uncover and continue baking for an additional 5 to 7 minutes to allow the cheese to melt thoroughly.