In a large skillet, cook the chicken over medium heat until lightly browned. Remove and set aside.
In the same skillet, sauté the onion and garlic until fragrant.
Add the rinsed rice, chicken stock, and water, bringing it to a simmer. Cover and cook until the rice is nearly tender.
Stir in the chopped broccoli and let it steam with the rice.
Add the milk and half of the shredded cheese, stirring until the cheese melts into a creamy sauce.
Return the cooked chicken to the skillet, mix well, and sprinkle the remaining cheese on top.
Cover and let the cheese melt before serving warm.