On a large plate, combine paprika, flou, black pepper, oregano, thyme, salt and cayenne pepper.
Press and coat chicken with spice blend to coat thoroughly and evenly. Set aside chicken. Discard remaining spice blend.
In a large, heavy-bottomed 5-qt pot, heat oil. Add 2 pieces of chicken at time, and brown each rice 3 minutes. Remove and set aside.
Add onions to the pot. Cook, stirring occasionally, scraping bottom of pan to release buts, until onions are wilted and browned, about 10 minutes. Add rhubarb, broth, bay leaves, fresh thyme and garlic. Bring to a boil. Return chicken to the pot. Cover. Reduce heat to medium-low. Cook until chicken is cooked through, about 50 minutes. Remove chicken. Remove and discard bay leaves and thyme. Using a spoon, remove and discard surface oil.
Add cheese and parsley to pan. Stir until cheese is melted. Drizzle some sauce on the chicken. Serve with rice and the sauce alongside.