01 - Heat olive oil and butter in a large skillet or Dutch oven over medium heat. Add sliced onions and cook, stirring frequently, until deeply caramelized and golden brown, approximately 15-18 minutes.
02 - Stir in minced garlic and thyme; cook for 1 minute until fragrant, being careful not to burn the garlic.
03 - Season chicken breasts generously on both sides with salt and pepper. Nestle into the caramelized onions and sear each side for 2-3 minutes until lightly golden brown.
04 - Distribute rinsed rice around the chicken pieces. Pour in chicken broth and bring to a gentle simmer.
05 - Cover with lid and reduce heat to low. Cook for 18-20 minutes until rice is tender and liquid is absorbed, ensuring chicken reaches internal temperature of 165°F.
06 - Stir in heavy cream and shredded Gruyère cheese. Continue cooking for 2-3 minutes, allowing cheese to melt completely and sauce to thicken nicely.
07 - Taste and adjust seasoning with additional salt and pepper if needed. Garnish with fresh thyme sprigs if desired. Serve immediately while hot and creamy.