Shred the rotisserie chicken into bite-sized pieces and set aside.
In a large skillet, heat olive oil over medium heat and sauté the sliced onions until caramelized and golden brown, about 15-20.
Cook the orzo in boiling salted water according to package instructions, about 8-10, until al dente. Drain and set aside.
In a large mixing bowl, combine shredded chicken, cooked orzo, chicken broth, heavy cream, garlic powder, dried thyme, salt, black pepper, and caramelized onions. Mix well.
Pour the mixture into a greased 9x13-inch baking dish, cover with foil, and bake at 375°F for 25. Remove foil, sprinkle cheeses on top, and bake uncovered for an additional 15-20 until cheese is bubbly and golden brown.
Let the casserole cool for 5 before serving and garnish with fresh parsley.