Prepare the Vegetables: In a large, heavy-bottomed pot, melt two tablespoons of the unsalted butter over medium heat. Introduce the chopped mushrooms and diced onion to the pot. Sauté the mixture for approximately 6-7 minutes, or until the vegetables achieve a caramelized state. Following this, incorporate the minced garlic and continue to cook for an additional minute. Once done, remove the vegetables from the pot and set aside.
Cook the Rice: Utilize the same pot to melt the remaining two tablespoons of butter. Add the long-grain rice, thyme, and salt, stirring the ingredients together to evenly coat the rice with butter. Cook for about one minute, allowing the rice to toast slightly, which will imbue it with a nutty flavor. Gradually pour in half a cup of the beef broth to deglaze the pot, carefully scraping any browned bits from the bottom to infuse the rice with additional flavor.
Simmer the Rice: Introduce the remaining beef broth into the pot and raise the heat to bring the mixture to a simmer. Once achieved, reduce the heat to low, cover the pot, and allow the rice to cook undisturbed for 15 minutes, or until it is tender and has absorbed most of the broth.
Finalize the Dish: Remove the pot from the heat. Reintroduce the previously sautéed mushrooms and onions, gently folding them into the cooked rice. Cover the pot once more and let the dish stand for 5 minutes to allow the flavors to meld together. Taste and adjust the seasoning as necessary. If desired, garnish with freshly chopped parsley before serving.