Start by preheating your oven to 375°F (190°C). Pat your chicken thighs dry and season them well with salt and pepper. Heat one tablespoon of olive oil in your oven-safe skillet over medium-high heat. Sear the chicken, skin-side down, for about 5–6 minutes until the skin is nicely golden. Flip and cook for another 2 minutes. Set the chicken aside for now.
In the same skillet, pour in the rest of the olive oil and drop in the butter. Add the thinly sliced onions with a pinch of salt. Let them cook slowly over medium-low heat. Stir every few minutes. It’ll take about 25–30 minutes for the onions to become deeply golden and sweet. In the last 2 minutes, add your garlic and thyme.
Now, sprinkle flour over your caramelized onions. Stir well so the flour coats everything evenly—cook it for one minute to remove the raw taste. Pour in the white wine (or broth), scraping the bottom to release all those tasty browned bits. Let it simmer for 2 minutes. Then add the beef broth and simmer for another 3–4 minutes to thicken slightly.
Next, stir in the rinsed white rice. Make sure it’s evenly mixed with the onion mixture. Season with salt and pepper again if needed.
Now comes the layering. Place the seared chicken thighs on top of the rice and onion mixture, skin-side up. Cover the skillet with foil or a tight-fitting lid and bake for 35 minutes.
After that, remove the cover and sprinkle on the Gruyère and Parmesan cheese. Bake uncovered for another 10–15 minutes until the cheese melts and becomes golden and bubbly. Make sure the chicken reaches an internal temperature of 165°F (75°C).
Let it rest for 10 minutes before sprinkling with fresh parsley and serving.