Step 1: Preheat your oven to 3750F (1900C).
Step 2: In a large, oven-safe Dutch oven or deep skillet, heat olive oil and butter over medium-low heat. Add the thinly sliced onions and cook, stirring occasionally, for 20-30 minutes, until they are deeply caramelized and a rich golden brown. Remove onions from the pot and set aside in a bowl.
Step 3: Increase the heat to medium-high. Add the ground beef to the same pot and cook, breaking it up with a spoon, until it's fully browned. Drain any excess grease.
Step 4: Return the caramelized onions to the pot with the beef. Add the minced garlic, dried thyme, Worcestershire sauce, salt, and pepper. Stir well and cook for 1 minute until fragrant.
Step 5: Stir in the rinsed uncooked rice and the beef broth. Bring the mixture to a simmer, then reduce the heat to low, cover the pot, and cook for 15-20 minutes, or until most of the liquid has been absorbed and the rice is nearly tender. Do not stir too much during this stage.
Step 6: Remove the pot from the heat. Top the casserole evenly with the shredded Gruyère or Swiss cheese.
Step 7: Transfer the Dutch oven (or pour into a 9x13 inch baking dish if your skillet is not oven-safe) to the preheated oven. Bake for 20-25 minutes, or until the cheese is melted, bubbly, and golden brown.
Step 8: Let the casserole rest for 5-10 minutes before serving to allow the flavors to meld and the rice to set.