Generously season both sides of the chicken thighs with salt and pepper and squeeze the juice of 1 lime over the chicken.
Heat oil over medium-high heat in a large, oven-safe pan with a lid. Add chicken thighs and brown on both sides, about 8-10 minutes (they won't be cooked all the way through). Remove to a plate.
Reduce heat to medium and add onion and garlic. Season with salt and pepper and cook until starting to brown, about 3 minutes. Add wine and scrape up any browned bits that have stuck to the bottom.
Add spinach, broth, rice, beans, tomatoes, crema, and paprika. Stir to combine and bring to a boil. Place chicken pieces on top and reduce heat to low. Cover and cook until rice is tender, about 20 minutes.
Heat broiler to high. Remove chicken and rice from the heat and remove lid. Unroll the wheel of Oaxaca cheese and arrange it on top of the chicken and rice, trying to cover as much of the dish as possible. Broil until cheese is melted and browned in spots, about 4 minutes.
Sprinkle with parsley and serve.