In a large oven-safe skillet over medium heat, melt the butter and olive oil. Add the sliced onions and cook, stirring occasionally, for 25-30 minutes until they are deeply caramelized and sweet. Be patient, as this step builds the primary flavor.

Push the onions to one side of the skillet. Add the cubed chicken to the empty side and season with salt and pepper. Cook until the chicken is browned on all sides, about 5-7 minutes.

Stir the minced garlic and fresh thyme into the chicken and onions. Cook for 1 minute until fragrant. If using, pour in the white wine to deglaze, scraping any browned bits from the bottom of the pan. Allow the wine to cook for about 1 minute.

Add the uncooked orzo to the skillet and stir constantly for 1-2 minutes to toast it lightly.

Pour in the beef broth and heavy cream. Stir everything together and bring to a gentle simmer. Reduce the heat to low, cover the skillet, and let it cook for 10-12 minutes, until the orzo is nearly cooked through and has absorbed most of the liquid.

Preheat your oven's broiler. Remove the skillet from the heat. Stir in half of the shredded Gruyère cheese and all of the Parmesan cheese until melted and creamy. Taste and adjust seasoning with salt and pepper if needed.

Sprinkle the remaining Gruyère cheese evenly over the top of the casserole. Place the skillet under the broiler for 2-4 minutes, watching closely until the cheese is melted, bubbly, and golden brown.

Let the casserole rest for 5 minutes before serving. Garnish with fresh thyme if desired.