Step 1: Season and Sear the Chicken

1. Season the Chicken: Pat the chicken breasts dry with paper towels. Season both sides with salt, pepper, garlic powder, and dried thyme.
2. Sear the Chicken: In a large, oven-safe skillet or Dutch oven, heat the olive oil over medium-high heat. Add the chicken breasts and sear for 3-4 minutes on each side, until golden brown. Remove the chicken from the skillet and set aside. The chicken will finish cooking later with the rice.

Step 2: Caramelize the Onions

1. Melt the Butter: In the same skillet, melt the butter over medium heat. Add the sliced onions and sugar, stirring to coat the onions in the butter.
2. Cook the Onions: Cook the onions for about 20 minutes, stirring occasionally, until they are deeply caramelized and golden brown. If the onions start to stick, add a splash of water or broth to deglaze the pan and prevent burning.
3. Add Garlic and Balsamic: Add the minced garlic and cook for another minute. Stir in the balsamic vinegar and cook for an additional 2 minutes, scraping up any browned bits from the bottom of the skillet.

Step 3: Prepare the Sauce and Rice

1. Make the Sauce: Sprinkle the flour over the caramelized onions and stir well to combine. Cook for 1-2 minutes to cook out the raw flour taste.
2. Add Broths: Gradually pour in the beef broth and chicken broth, stirring constantly to prevent lumps. Add the Worcestershire sauce and dried thyme. Bring the mixture to a simmer and cook for 5 minutes, allowing the flavors to meld.
3. Add the Rice: Stir in the uncooked rice, ensuring it is evenly distributed in the sauce.

Step 4: Bake the Dish

1. Return the Chicken: Nestle the seared chicken breasts into the skillet, spooning some of the onion sauce over the top.
2. Bake: Cover the skillet with a lid or aluminum foil and bake in a preheated oven at 375°F (190°C) for 25-30 minutes, or until the rice is tender and the chicken is cooked through (internal temperature of 165°F/74°C).

Step 5: Add Cheese and Broil

1. Top with Cheese: Remove the skillet from the oven and uncover. Sprinkle the shredded Gruyère cheese over the chicken and rice.
2. Broil: Place the skillet under the broiler for 3-5 minutes, or until the cheese is melted and bubbly.

Step 6: Serve and Enjoy

1. Garnish and Serve: Garnish the French Onion Chicken & Rice with chopped fresh parsley and serve hot. Enjoy this comforting, flavorful dish with a side salad or crusty bread.