1. Preheat your oven to 350°F (175°C).
2. In a large oven-safe skillet, heat the olive oil over medium heat. Add the onions and garlic, sautéing until they are translucent and fragrant, about 3-4 minutes.
3. Add the sliced mushrooms and cook until they release their moisture and start to brown, roughly 5 minutes.
4. Stir in the uncooked rice, allowing it to toast slightly for about 2 minutes. This will add a delightful nutty flavor to your dish.
5. Pour in the chicken broth and milk, stirring to combine. Add the salt, pepper, and thyme.
6. Bring the mixture to a simmer, then reduce the heat to low and cover. Allow it to cook for 15 minutes.
7. Stir in the cooked chicken and half of the Parmesan cheese until well combined.
8. Transfer the skillet to the preheated oven and bake for 20 minutes, or until the rice is tender and the liquid is absorbed.
9. Remove from the oven, sprinkle the remaining Parmesan cheese on top, and return to the oven for another 5 minutes, or until the cheese is golden and bubbly.
10. Garnish with chopped parsley before serving.

This dish is a family favorite in my home, where it never fails to bring everyone to the table with eager anticipation.