Heat the olive oil in a large non-stick pan over medium heat. Add the sliced onions and a pinch of salt. Saute the onions until they become slightly caramelized, stirring occasionally.

To the pan, add the balsamic vinegar, Worcestershire sauce, and dried thyme. Stir to combine, then reduce the heat to medium-low.

Cook the onions for approximately 20 minutes, or until they are fully caramelized and have a jam-like consistency. Set the caramelized onions aside.

In a shallow dish, whisk together the all-purpose flour, salt, black pepper, and paprika.

Dredge each chicken cutlet in the flour mixture, ensuring both sides are coated evenly. Set the coated cutlets aside. Reserve 1 tablespoon of the flour mixture for later use.

In the same skillet used for the onions, melt the butter over medium-high heat. Once the butter has melted, add the coated chicken cutlets to the pan.

Cook the chicken cutlets for approximately 3-4 minutes on each side, or until they are cooked through and nicely browned. Remove the cooked chicken from the pan and set aside.

Whisk the remaining 1 tablespoon of flour mixture into the beef broth or stock. Pour the broth into the pan and deglaze it over medium-low heat, scraping up any browned bits from the bottom of the pan. Cook until the sauce has thickened.

Return the cooked chicken cutlets to the pan with the thickened sauce. Simmer for an additional 5-8 minutes, allowing the flavors to meld together.

Divide the caramelized onions on top of the chicken in the pan. Sprinkle the shredded mozzarella cheese evenly over the onions.

Cover the pan and continue to simmer for another 10 minutes, or until the cheese has melted and is bubbly.

Garnish with fresh parsley, if desired, and serve the chicken cutlets with the flavorful caramelized onion and cheese topping.

Enjoy this delicious and savory french onion chicken!