Make the Sofrito. Add the green bell pepper, onion, garlic cloves and cilantro to a food processor or high-speed blender. Blend until a smooth, slightly textured sauce forms. Measure out ½ to ¾ cup for the recipe and reserve any extra for later use.
Season the Chicken. Pat the chicken completely dry with paper towels. Season all sides generously with sazon, salt and black pepper, including underneath the skin.
Sear the Chicken. Heat a wide skillet or braising pan over medium heat and add the olive oil. Place the chicken skin side down and sear for 5 to 6 minutes until the skin is deeply golden and the fat has rendered. Flip and cook for another 2 minutes. Remove the chicken to a plate.
Cook the Tomato Paste. In the same pan, add the tomato paste and cook for 1 minute, stirring to slightly caramelize and deepen the flavor.
Cook the Sofrito. Add ½ to ¾ cup of the prepared sofrito to the pan. Stir and cook for 2 to 3 minutes, allowing the vegetables to soften and the flavors to concentrate.
Build the Sauce. Stir in the chopped tomatoes with their juices, black beans and 1 cup chicken stock. Season lightly with salt and pepper. The liquid should come about halfway up the chicken once it is returned to the pan. Add a little more stock if needed.
Simmer the Chicken. Nestle the chicken back into the pan, skin side up, keeping the skin above the sauce. Bring to a gentle simmer. Cover with the lid slightly ajar and cook for 28 to 30 minutes.
Reduce the Sauce. Remove the lid completely and continue simmering for another 10 minutes to slightly reduce and thicken the sauce. The chicken should be fully cooked and tender.
Garnish and Serve. Garnish with chopped fresh cilantro and serve hot with white rice.