Slowly cook sliced onions in butter and olive oil over medium-low heat until deeply caramelized and golden.
Season chicken with salt, pepper, and thyme, then sear in a hot pan until golden on the outside.
Toast orzo in the same pan, then add chicken broth and simmer until partially cooked.
Stir in cream or milk, garlic, and some cheese to form a creamy sauce.
Combine onions, chicken, and orzo mixture in a baking dish.
Top with remaining cheese and bake at 180°C (350°F) for 25–30 minutes until bubbly and golden.
Let rest for 5–10 minutes before serving.