Preheat the oven to 350°F (175°C).
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and minced garlic, and sauté until the onion is translucent.
Add the ground beef to the skillet, breaking it up with a spoon. Cook until browned and no longer pink. Drain excess fat if necessary.
Stir in the sliced mushrooms, salt, black pepper, and thyme. Cook for another 5 minutes until mushrooms are tender.
In a large mixing bowl, combine the cooked rice, cream of mushroom soup, beef broth, and sour cream. Mix until well combined.
Add the beef and mushroom mixture to the rice mixture, and stir until everything is evenly mixed.
Transfer the mixture to a greased 9x13 inch baking dish. Spread it evenly and top with shredded cheddar cheese.
Bake in the preheated oven for 30 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let it sit for 5 minutes before serving.