Step 1: In a large oven-safe skillet or Dutch oven, melt butter over medium-low heat. Add sliced onions and cook, stirring occasionally, for 20-25 minutes until deeply caramelized and golden brown. Be patient, as this step is crucial for flavor.
Step 2: Push onions to one side of the skillet. Add ground beef to the other side and cook over medium-high heat, breaking it up with a spoon, until browned. Drain any excess fat.
Step 3: Stir the minced garlic into the beef and onions and cook for 1 minute until fragrant.
Step 4: Sprinkle flour over the beef and onion mixture. Cook, stirring constantly, for 2 minutes to create a roux.
Step 5: Gradually whisk in 3 cups of beef broth, stirring until no lumps remain and the sauce begins to thicken. Stir in dried thyme, Worcestershire sauce, salt, and pepper.
Step 6: Stir in the uncooked long-grain white rice and the remaining 1 cup of beef broth. Bring the mixture to a gentle simmer.
Step 7: Remove the skillet from heat. Stir in 1 cup of shredded Gruyère cheese until melted and combined. Pour the mixture into a 9x13 inch baking dish if not using an oven-safe skillet.
Step 8: Top evenly with the remaining 1/2 cup of shredded Gruyère cheese.
Step 9: Cover the baking dish tightly with foil. Bake in a preheated oven at 375°F (190°C) for 30 minutes. Remove the foil and bake for an additional 10-15 minutes, or until the rice is tender and the cheese is bubbly and lightly golden.
Step 10: Let the casserole rest for 5-10 minutes before serving. Garnish with fresh parsley, if desired.