Set your oven to 350°F to start warming up.
In a broiler-safe 9x13-inch dish, mix the rice, beef broth, vinegar, garlic powder, thyme, onion powder, salt, pepper, half a cup of Gruyère cheese, and three-quarters of the half-and-half until everything is well combined.
Heat butter in a large skillet over high heat, then add mushrooms and shallots, cooking and stirring every so often until the shallots soften and mushrooms brown lightly, about 8 minutes.
Take the skillet off the heat and stir in the shredded chicken, softened cream cheese, and the remaining half cup of half-and-half until the cream cheese melts into a creamy mixture.
Pour this creamy mushroom and chicken mixture into the rice mixture and fold everything together gently.
Cover the casserole dish tightly with foil and bake in the preheated oven until it starts bubbling, roughly 45 minutes.
Carefully remove the foil, give the casserole a good stir to make it creamy, then sprinkle the remaining half cup of Gruyère cheese evenly on top.
Return it to the oven uncovered and bake until the liquid mostly absorbs and the rice is tender, 30 to 35 minutes more.
Turn your oven setting to broil and broil the casserole until the cheese turns a golden, bubbly brown, usually 3 to 4 minutes.
Finish by garnishing with fresh thyme leaves before serving, if you like.
