Heat two tablespoons of the olive oil in a large skillet over medium heat and cook the onions until soft. Season the chicken pieces with salt and pepper.
Turn up the heat to medium-high and add the chicken to the pan, cooking until browned. Stir in the minced garlic and let it cook for about one minute.
Slide the chicken to one side of the pan. Add the remaining tablespoon of olive oil to the other side and toast the uncooked rice in the oil for a couple of minutes.
Pour in the chicken broth and bring the mixture to a boil. Reduce the heat to a simmer and cover the pan.
Let the chicken and rice cook for about 12 minutes with the lid on.
Scatter the broccoli florets evenly over the top and stir gently to combine everything.
Cover again and cook on low heat for another 8 minutes, or until both the rice and broccoli are tender.
Take the skillet off the heat and stir in half a cup of shredded cheddar cheese until melty.
Sprinkle the remaining cheese over the dish, cover with the lid, and let it rest for 1-2 minutes to allow the cheese on top to melt fully.