Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Season the bite-size chicken pieces with 1/2 teaspoon salt and 1/4 teaspoon black pepper, then add the chicken and the diced onion to the skillet.
Cook, stirring occasionally, until the chicken is lightly browned and cooked through and the onion is tender, about 6 minutes.
Add minced garlic, uncooked white rice, chopped broccoli, and a pinch of red pepper flakes to the skillet and stir to combine.
Pour in 2 cups chicken stock, bring the mixture to a boil, then reduce heat to a simmer and cover the skillet.
Simmer, covered, until the rice is tender and the liquid is absorbed, about 17 minutes.
Stir in 1/2 cup sour cream and 1/2 cup of the shredded cheese until the mixture is creamy.
Sprinkle the remaining 1 cup shredded cheese on top, replace the lid, and let sit over low heat until the cheese melts, about 2 minutes.
Serve hot.
