Stir together the pepper, lemon zest, oregano, and 1/2 teaspoon of the salt in a small bowl. Rub the chicken with the lemon-pepper mixture. Place in a 5- to 6-quart slow cooker. Add the stock and lemon juice to the slow cooker. Top evenly with the lemon slices. Cover and cook on LOW 1 hour and 30 minutes. Uncover the slow cooker and place the Broccolini on top of the chicken. Sprinkle with the remaining 1/4 teaspoon salt. Cover and cook until the chicken and vegetables are tender, about 2 more hours.