Add liquids and seasonings to a slow cooker. In a 6 quart or large slow cooker, add the brown rice, white onion, salt, pepper, garlic, Italian seasoning, and condensed soup. Next, add the dijon mustard and chicken stock and stir to combine.
Add chicken and cook. Add the cut chicken, mix well, and cook on high for 2 hours or until the chicken is cooked through and tender.
Add broccoli. When the chicken is cooked, add the cut broccoli and cook for another 1-2 hours until the rice has absorbed most of the liquid and the broccoli is tender.
Add cheese and serve. Finally, stir in the parmesan cheese and white cheddar cheese until thoroughly mixed and melted. Serve immediately.