In a large skillet over medium heat, heat the olive oil. Add the sliced onion and cook, stirring occasionally, until caramelized (about 15-20 minutes). Add the minced garlic and cook for an additional 2-3 minutes until fragrant.
In a large mixing bowl, combine the cooked orzo, shredded chicken, chicken broth, caramelized onions and garlic, thyme, rosemary, soy sauce, salt, and pepper. Mix thoroughly.
Transfer the mixture to a greased 9x13-inch baking dish.
Sprinkle the shredded Gruyere and mozzarella cheeses evenly over the top of the orzo mixture.
Bake in the preheated oven for 25-30 minutes, or until the cheese is bubbly and golden.
Remove from the oven and let it cool for a few minutes. Garnish with fresh parsley before serving.
Notes
Let the casserole cool for a few minutes before serving.