Mix lime juices and ginger. Allow to marinate for 1 hour. Pound chicken very thin. Cut off white portion of scallions and chop the green finely. Place chicken in pan, pour lime juice marninade over, add chopped scallions, carrot, celery and leek. Cover and refrigerate for 12 hours. Remove chicken, sprinkle with salt and pepper. Heat butter in skillet and saute chicken until golden brown on both sides. Remove and set aside. Add white portion of scallions to skillet and saute for 5 minutes. Strain the vegetables from the marinade and add to the skillet, saute for 5 minutes. Add marinade and simmer until liquid has evaporated. Add chicken stock and reduce by half. Add half and half and reduce to sauce consistency. Swirl in butter. Arrange chicken on plates and serve topped with sauce.