1. To prepare rice, heat a medium saucepan over medium-high heat. Add oil to pan; swirl to coat. Add onion and next 3 ingredients (through thyme); sauté 4 minutes. Add rice, paprika, 1/4 teaspoon red pepper, and garlic; sauté 1 minute. Add 2 cups water and 1/4 teaspoon salt; bring to a boil. Reduce heat, cover, and simmer 12 minutes. Let stand 5 minutes.
2. Heat a medium skillet over medium-high heat. Coat pan with cooking spray. Add livers; sauté for 4 minutes or until lightly browned and cooked through. Stir in green onions. Add liver mixture and hot pepper sauce to rice; fluff with a fork.
3. Preheat oven to 400°.
4. To prepare chicken, combine cumin and the next 5 ingredients (through 1/4 teaspoon red pepper); rub evenly over chicken. Heat a large ovenproof skillet over medium-high heat. Add oil to pan; swirl to coat. Add chicken to pan; cook 3 minutes. Turn chicken; place pan in oven. Bake at 400° for 6 minutes or until chicken is done. Remove chicken from pan. Add broth to pan; bring to a boil. Cook until liquid is reduced to 1/4 cup (about 2 minutes). Spoon sauce over chicken; serve with rice.