Place a large skillet over medium-high heat and add olive oil. Add onions, garlic and diced chicken. Season with salt and pepper and sauté, stirring frequently, until no pink remains.
Sprinkle flour over chicken mixture and stir to combine. Cook flour for 30 seconds before adding chicken broth. Stir until flour is completely dissolved in the broth then add milk, rice and chicken bouillon. Stir to dissolve bouillon and distribute rice evenly inside the skillet.
Bring liquid to a boil then reduce heat to low and simmer, uncovered and undisturbed, for 15–18 minutes or until rice is tender and liquid is mostly absorbed.
Add 1 cup cheddar cheese and broccoli florets to skillet and stir gently to combine. Do not stir too much or the rice will disintegrate.
Taste for seasoning and add salt and pepper as necessary. Continue cooking for an additional 2 minutes.
Top with remaining ½ cup shredded cheese, remove from heat and allow to rest for 5 minutes before serving.