Heat oil or butter in a large skillet or pot over medium heat. Add the sliced onions and cook, stirring occasionally, until golden brown and caramelized, about 15 to 20 minutes.
Add minced garlic and thyme; cook for 1 more minute until fragrant.
Add ground beef to the pot with the onions, breaking it up as it cooks. Brown the beef until fully cooked.
Season the beef mixture with salt, pepper, and Worcestershire sauce, stirring well.
Stir in the rice, ensuring it is well mixed with the beef and onions.
Pour in the beef broth and bring the mixture to a boil.
Reduce heat to low, cover the pot, and simmer for 18 to 20 minutes, or until the rice is tender and liquid is absorbed.
Fluff the rice with a fork. Top with shredded cheese if desired and allow it to melt.
Garnish with fresh parsley and serve warm.