In a large skillet, heat olive oil over medium heat. Add thinly sliced onions and a pinch of salt. Cook for about 15-20 minutes, stirring occasionally, until the onions are caramelized and golden brown. Add minced garlic in the last 2 minutes of cooking, then remove the onions and garlic from the skillet and set aside.
In the same skillet, increase the heat to medium-high. Season the chicken thighs with salt, pepper, and dried thyme. Sear the chicken for about 5-6 minutes on each side until golden brown. Remove the chicken from the skillet and set aside.
In the skillet, add uncooked rice and stir to coat it in the remaining juices. Pour in the chicken broth and balsamic vinegar. Bring the mixture to a boil.
Lower the heat to a simmer and nestle the seared chicken thighs back into the skillet. Cover and cook for about 20 minutes, or until the rice is tender and has absorbed most of the liquid.
Stir in the heavy cream and caramelized onions into the skillet. If using, sprinkle shredded cheese over the top and cover again for another 5 minutes until the cheese is melted and bubbly.
Once done, sprinkle fresh parsley on top for garnish. Serve hot directly from the skillet or transfer to individual plates.
Notes
Optional cheese can be added for extra creaminess.