Heat 1 tablespoon of oil in a deep 12-inch skillet with a lid over medium heat. Lightly season the chicken with salt.
Add the chicken pieces in a single layer and cook for 3–4 minutes until lightly browned. Flip and cook another 3–4 minutes until the chicken reaches an internal temperature of 165°F. Transfer the chicken to a bowl and set aside.
Add the remaining tablespoon of oil to the skillet. Stir in the diced onion, carrot, and a pinch of salt. Cook for about 5 minutes until softened.
Add the rice and minced garlic. Stir well so the rice is coated and cook for about 1 minute.
Slowly pour in the chicken broth while stirring and scrape up any browned bits from the bottom of the pan. Bring the mixture to a boil.
Once boiling, reduce the heat to a simmer. Cover and cook for 10 minutes.
Stir in the broccoli, cover again, and cook another 3–5 minutes until the rice is tender and the broccoli is cooked.
Return the cooked chicken to the skillet and stir in the shredded cheddar cheese. Mix until the cheese melts and everything is evenly combined.
Taste and adjust the salt if needed. Remove from heat and let the Cheesy Chicken Broccoli Rice rest with the lid on for about 10 minutes before serving.