Dice the chicken into small pieces and season with salt and pepper.
Warm 1 tablespoon of olive oil over medium heat in a large skillet or Dutch oven, then sauté the chicken for about 5 minutes until it’s nearly cooked through; set it aside on a covered plate.
Add the remaining olive oil to the pan and cook the diced onion and minced garlic for 3 minutes until they soften.
Stir in the uncooked rice and toast it lightly for a few minutes, stirring occasionally.
Pour in the milk and chicken broth, then add salt and pepper. Bring the mixture to a boil.
Cover the skillet, reduce the heat to medium-low, and let it simmer gently for 10 minutes, maintaining small bubbles.
Remove the lid and evenly distribute the chicken pieces and chopped broccoli on top of the rice without stirring. Cover again and simmer for another 10 minutes.
Check if the rice and broccoli are tender; if needed, add a bit more milk or broth, cover, and cook a few extra minutes.
Sprinkle shredded cheddar cheese over the casserole, cover, and let it sit off the heat for a few minutes until the cheese melts.
Serve the casserole warm, garnished with fresh chopped parsley if desired.