Chef John's Chicken and Rice

Preheat oven to 350 degrees F (175 degrees C). Season chicken pieces all over with salt and black pepper. Heat 2 tablespoons oil in a large skillet over high heat. Cook chicken in hot oil until browned, 4 to 6 minutes per side. Pour water over chicken into the skillet and remove from heat. Heat 1 tablespoon olive oil in a large, heavy pot or Dutch oven over medium heat. Cook and stir onion in hot oil until slightly translucent and softened, about 5 minutes. Add olives, garlic, paprika, capers, cumin, oregano, and cayenne pepper; cook and stir until fragrant, about 1 minute. Stir red bell pepper, green bell pepper, sugar, and kosher salt into the onion mixture; cook and stir until mixture is just combined. Add tomato paste; cook and stir until tomato paste is just toasted, about 1 minute. Pour rice into onion mixture and stir until rice is completely coated in onion mixture. Add chicken broth; stir. Place chicken pieces on top of rice, pressing down lightly until each piece is almost completely immersed in the broth. Pour any accumulated juices from the skillet into the pot. Bring mixture to a simmer and cover the pot with an oven-proof lid. Bake in the preheated oven until chicken no longer pink at the bone and rice is soft, about 30 minutes. An instant-read thermometer inserted into the chicken near the bone should read 165 degrees F (74 degrees C).