1-Melt the butter in a 12-inch cast iron or heavy-bottomed skillet over medium heat. Add the sliced onions, fresh thyme leaves, 1 teaspoon of the kosher salt, and black pepper. Cook, stirring frequently and adjusting heat as needed, until the onions are soft and deeply golden-brown, about 32 to 36 minutes.

2-Pour in the dry white wine, scrape up any browned bits from the bottom, and stir until the wine evaporates. Then, transfer the onions to a plate to set aside.

3-Add the long-grain white rice to the skillet and cook, stirring occasionally, until it becomes toasty, about 1 minute. Stir in the chicken broth, milk, and the remaining 1 teaspoon of kosher salt. Bring the mixture to a boil, stirring occasionally, then reduce heat to medium-low, cover, and cook for 5 minutes.

4-Stir in the bite-size pieces of chicken, making sure they are evenly distributed in the rice. Cover and simmer, stirring occasionally, until the rice is tender and the chicken is cooked through, about 10 to 12 minutes. While this cooks, get your broiler ready.

5-Stir the caramelized onions and half of the shredded Gruyère cheese into the rice mixture. Taste and adjust seasoning with salt and pepper as needed. Sprinkle the remaining Gruyère evenly on top and broil until the cheese turns golden-brown in spots, about 3 to 4 minutes. Finish with a garnish of fresh thyme and a bit more black pepper before serving.