Heat two tablespoons of olive oil in a large skillet over medium heat and cook the diced onion until softened.
Season the chicken pieces with salt and pepper, then turn the heat to medium-high and add the chicken to the skillet.
Cook the chicken until browned, then stir in the minced garlic and let it cook for about a minute.
Move the chicken to one side of the pan and add the remaining tablespoon of olive oil to the empty side.
Add the uncooked rice to the oil and toast it for a couple of minutes, stirring frequently.
Pour in the chicken broth and bring everything to a boil, then reduce the heat to low and cover the pan with a lid.
Let the chicken and rice simmer covered for about 12 minutes.
Scatter the broccoli florets evenly on top of the mixture and gently stir to combine.
Cover again and continue to cook for another 8 minutes on low heat, until both broccoli and rice are tender.
Take the pan off the heat and mix in half a cup of the shredded cheddar cheese.
Sprinkle the remaining cheese over the top, cover the skillet, and allow it to sit for 1-2 minutes so the cheese melts perfectly.