Cut the chicken breasts into 1-inch cubes and season with salt and black pepper.
Heat the olive oil in a large oven-safe skillet or Dutch oven over medium-high heat.
Add the chicken and brown it on all sides for about 5–7 minutes. The chicken does not need to be fully cooked at this stage because it will finish cooking later.
If necessary, brown the chicken in two batches to avoid overcrowding the pan. Transfer the browned chicken to a plate.
Add the chopped onion to the same pan and cook for about 5 minutes, until softened and translucent.
Stir in the minced garlic and cook for about 30 seconds, until fragrant.
Return the browned chicken to the pan. Add the rinsed rice, chicken stock, and water. Stir to combine and bring the mixture to a boil.
Reduce the heat to low, cover, and cook for about 10 minutes.
Add the chopped broccoli and stir gently. Cover again and continue cooking until the rice is tender and the chicken is cooked through, stirring occasionally as needed.
Preheat the oven to 425°F (220°C).
Once the rice is cooked, stir in the milk.
Add 1 cup of shredded cheddar cheese and fold it through the rice and chicken mixture.
Sprinkle the remaining 1 cup of cheddar evenly over the top.
Transfer the skillet to the oven and bake for 10–15 minutes, or until the cheese is melted, bubbling, and lightly golden.
Let the casserole rest for a few minutes before serving. This helps the creamy rice mixture settle slightly.