In a large oven-safe skillet, melt 2 tablespoons of unsalted butter with 1 tablespoon of olive oil over medium heat. Add 3 large sliced yellow onions, along with a pinch of sugar and salt. Cook slowly for 30-40 minutes, stirring occasionally, until the onions are deeply golden and caramelized. In the last minute of cooking, add 2 minced garlic cloves for aromatic depth, then remove from heat.

In a separate skillet, heat a tablespoon of olive oil over medium-high heat. Season 2 cups of shredded cooked chicken with salt and black pepper, and add to the skillet. Sear the chicken for about 5-7 minutes, stirring occasionally, until it's golden brown but not fully cooked through.

Return to the caramelized onions, and pour in 1 cup of low-sodium chicken broth to deglaze the skillet, scraping up any flavorful bits stuck to the bottom. Stir in 1 cup of orzo pasta, 1 cup of heavy cream, and a teaspoon of dried thyme. Add the browned chicken and mix well. Simmer for 5-7 minutes until the orzo absorbs some of the liquid and is slightly tender.

Preheat your oven to 375°F (190°C). Stir in half of the 1 cup of shredded mozzarella cheese into the mixture until melted and combined. Transfer the casserole to the oven, sprinkle the top with the remaining cheese and ¼ cup of grated Parmesan cheese, and bake for 20-25 minutes.

Once out of the oven, allow the French Onion Chicken Orzo Casserole to rest for 5-10 minutes. Optionally, garnish with fresh thyme or parsley. Enjoy this comforting dish!