Set your oven to 350°F to preheat.
In a 9-by-13-inch broiler-safe baking dish, mix the rice, beef broth, vinegar, garlic powder, fresh thyme, onion powder, salt, pepper, half of the Gruyère cheese, and three-quarters of the half and half until well combined.
Heat butter in a large skillet over high heat until melted.
Add the sliced mushrooms and chopped shallots to the skillet and cook, stirring occasionally, until the shallots become tender and the mushrooms start to brown, roughly 8 minutes.
Remove the skillet from heat and stir in the shredded rotisserie chicken, softened cream cheese, and the remaining half and half until the mixture is creamy and smooth.
Pour this mushroom and chicken mixture into the baking dish and stir everything together thoroughly.
Cover the baking dish tightly with foil and place it in the oven to bake for about 45 minutes, until it starts bubbling.
Carefully remove the foil and give the casserole a good stir until it’s creamy.
Sprinkle the remaining Gruyère cheese evenly over the top.
Return the dish to the oven uncovered and bake for another 30 to 35 minutes, until the rice is tender and most of the liquid is absorbed.
Turn the oven setting to broil and cook for 3 to 4 minutes, or until the cheese topping is beautifully golden brown.
Garnish with extra thyme leaves before serving if you like.