Cut the chicken into small pieces and sprinkle with salt and pepper.
Warm 1 tablespoon of olive oil in a large skillet or Dutch oven over medium heat and cook the chicken for about 5 minutes until nearly done, then set aside covered.
Add the remaining olive oil to the pan and sauté the diced onion and minced garlic until they soften, around 3 minutes.
Stir in the uncooked rice and let it toast for a couple of minutes while stirring frequently.
Pour in the milk and chicken broth, then season with sea salt and black pepper. Bring the mixture to a boil.
Cover the pan, lower the heat to medium-low, and let it simmer gently with the lid on for 10 minutes.
Remove the lid and evenly place the cooked chicken and chopped broccoli over the rice without mixing. Cover again and simmer for another 10 minutes.
Check if the rice and broccoli are tender; if needed, add a splash of milk or broth, cover, and cook a few minutes more.
Sprinkle the shredded cheddar cheese on top, cover the pot, and let it sit off heat for a few minutes until the cheese melts.
Serve warm, garnished with chopped fresh parsley.
