Dice chicken, season thoroughly, and cook in a skillet until golden and 165°F internally.
Blend all cheese sauce ingredients until smooth. Add a splash of milk if needed.
Steam broccoli until tender.
Add broccoli, shredded cheese, and blended sauce to chicken. Stir over low heat until creamy.
Divide cooked rice into 8 containers. Top evenly with cheesy chicken and broccoli.