Drain soaked rice in a colander, and rinse well with cold water. Combine 2/3 cup rice, chopped chicken thigh, 2 tablespoons tomato paste, baharat, 2 teaspoons salt, 1/2 teaspoon black pepper, and cardamom in a medium bowl; stir until mixture is well combined. Set remaining soaked rice aside until ready to use.

Gently loosen the breast skin from the whole chicken using your fingers. Stuff rice mixture under breast skin (about 1/4 cup) and into chicken cavity (about 3/4 cup). Prick chicken skin using a fork or a sharp paring knife. Set aside.

Preheat oven to 350°F with rack positioned in bottom third of oven. Heat 2 tablespoons oil in a large nonstick pot or Dutch oven over medium-high. Add diced tomatoes, chopped onion, cinnamon, paprika, remaining 1/2 cup plus 2 tablespoons tomato paste, and remaining 1/2 teaspoon black pepper; cook, stirring occasionally, until mixture is fragrant and tomato paste darkens slightly, about 5 minutes. Remove from heat, and transfer to a medium bowl. Wipe pot clean.

Coat bottom of pot with 1 tablespoon oil. Fit a circle of parchment paper into bottom of oiled pot, and drizzle paper with remaining 1 tablespoon oil. Add diced tomato mixture, 4 cups water, tomato sauce, bouillon, and remaining 4 teaspoons salt; bring to a boil over high. Add reserved soaked rice; reduce heat to medium, and simmer, undisturbed, 20 minutes. Nestle chicken, breast side up, into center of rice mixture. Spoon some of the simmering liquid over chicken; cook over medium, undisturbed, 10 minutes.

Cover pot with lid, and transfer to preheated oven; roast until an instant-read thermometer inserted in thickest portion of breast registers 165°F, 1 hour and 20 minutes to 2 hours. Uncover pot; increase oven temperature to 425°F, and roast until chicken is browned in spots, about 10 minutes. Remove from oven, and let cool 20 minutes. To serve, carefully transfer chicken to a plate, and set aside. Invert pot onto a large round platter to release the rice; remove and discard parchment paper. Transfer chicken to the platter, nestling it into the center of the rice. (Alternatively, remove chicken from pot; set aside. Spoon rice onto large platter, placing crispy rice on top. Place chicken over rice, and serve.)