Position a rack in the center of the oven and preheat to 350°F (175°C). Lightly grease a 9-by-13-inch (23-by-33-cm) baking dish.

Combine the rice, water, and salt in a medium saucepan. Bring to a boil, reduce the heat to low, cover, and cook for 15 minutes. Remove from the heat and let it stand, covered, for 10 minutes before fluffing with a fork.

Heat the olive oil in a large skillet over medium heat. Add the sliced onions and cook for 18 to 22 minutes, stirring often, until deeply golden and soft. If the onions begin browning too quickly, reduce the heat slightly and add 1 tablespoon of water.

Add the ground beef to the skillet with the onions. Cook for 6 to 8 minutes, breaking the meat into small crumbles, until no pink remains and it reaches 160°F (71°C). Drain excess grease if necessary.

Stir in the garlic, Worcestershire sauce, thyme, onion powder, black pepper, and salt. Cook for 30 seconds until fragrant.

Sprinkle the flour over the beef mixture and stir for 1 minute. Gradually whisk in the beef broth. Simmer for 3 to 4 minutes until the mixture thickens slightly. Remove the skillet from the heat and stir in the sour cream and Dijon mustard until smooth.

Fold the cooked rice into the beef mixture until evenly combined. Spread the mixture into the prepared baking dish in an even layer.

Sprinkle the Gruyère evenly over the casserole, followed by the mozzarella.

Cover the dish loosely with foil and bake for 20 minutes until heated throughout.

Remove the foil and continue baking for 10 to 12 minutes until the cheese is melted, bubbling, and lightly golden around the edges.

Let the casserole rest for 10 minutes before serving. This allows the sauce to thicken slightly and makes serving easier.

Sprinkle with fresh parsley, if using, and serve hot.