01 - Heat olive oil and butter in a large skillet or Dutch oven over medium heat. Add the sliced onions and cook, stirring often, until deeply caramelized, about 15-18 minutes.
02 - Add minced garlic and thyme; cook for 1 minute until fragrant.
03 - Season chicken breasts on both sides with salt and pepper, then nestle into the caramelized onions. Sear each side for 2-3 minutes until lightly browned.
04 - Add the rinsed rice around the chicken, then pour in the chicken broth. Bring to a gentle simmer.
05 - Cover with a lid, reduce heat to low, and cook for 18-20 minutes until rice is tender and chicken is cooked through.
06 - Stir in the heavy cream and shredded Gruyère, allowing the cheese to melt and the sauce to thicken for 2-3 minutes.
07 - Taste and adjust seasoning as needed. Garnish with extra thyme if desired. Serve hot.