Preheat oven to 375°F (190°C). Heat olive oil in a large skillet over medium heat.
Add diced chicken, season with salt and pepper, and cook until browned. Remove and set aside.
In the same skillet, sauté onions, garlic, and mushrooms until softened. Add Arborio rice and stir for 2 minutes.
Pour in white wine (if using) and cook until absorbed. Add chicken broth, one cup at a time, stirring continuously, until the rice is tender and creamy.
Combine the chicken, rice mixture, and half of the Parmesan cheese in a baking dish.
Top with mozzarella and the remaining Parmesan. Bake for 20-25 minutes, until bubbly and golden.
Let rest for 10 minutes, garnish with fresh parsley, and serve.