Cut chicken breasts in half lengthwise parallel to the cutting board, so you get two thinner pieces of chicken. Season both sides of each piece of chicken with salt, pepper and one tablespoon of the dried thyme.

Heat a large sauté pan over medium heat. Add one tablespoon of avocado oil and then the chicken. Sear chicken for 4-5 minutes on each side, or until cooked to an internal temperature of 165°F. Remove chicken from pan and set aside.

To the sauté pan, add another tablespoon of oil, if needed. Add diced onions and sauté for 4-5 minutes, stirring continuously. Add a ½ cup of the chicken broth to the pan. Cook onions, stirring occasionally, until all the broth has evaporated and onions are soft and golden brown, about 15-18 minutes.

Add garlic, remaining one tablespoon of thyme and the orzo. Stir to mix in with the onions and toast ingredients for one minute. Add remaining 3 cups of chicken broth and cook orzo for 10-12 minutes, or until orzo is al dente. Stir orzo occasionally to prevent it from sticking to the pan.

Mix butter into the orzo. Slice chicken and place on top of the orzo. Add shaved gruyere to the top of each piece of chicken. Cover the pan with lid, reduce heat to medium-low and cook until the cheese has melted, about 10 minutes.