In a large saucepan, heat the olive oil over medium heat. Add the sliced onion and cook, stirring frequently, until the onions are caramelized and golden brown, about 15-20 minutes.
Add the minced garlic to the pan and sauté for another minute until fragrant.
Stir in the cooked chicken, chicken broth, thyme, rosemary, balsamic vinegar, salt, and pepper. Bring mixture to a gentle boil.
Add the orzo pasta to the pan. Stir well, ensuring the pasta is submerged in the liquid. Cook for about 5 minutes, stirring occasionally.
Remove from heat and stir in 1 cup of the Gruyère cheese, mixing until melted and combined.
Pour the mixture into a greased 9x13 inch baking dish. Top with the remaining ½ cup of Gruyère cheese.
Bake in the preheated oven for 20-25 minutes, or until the top is golden and bubbly.
Remove from oven and let cool for a few minutes before garnishing with fresh parsley.
Notes
Let the dish cool slightly before serving for better texture.