Combine first 10 ingredients in a blender, and process until smooth. Combine green onion mixture and chicken in a large zip-top plastic bag; seal and marinate in refrigerator 24 hours, turning bag occasionally.
Place potato in a saucepan, and cover with water; bring to a boil. Reduce heat, and simmer 15 minutes or until tender; drain. Cool.
Heat oil in a large nonstick skillet over medium heat. Add chicken and marinade; cook 5 minutes on each side or until done. Remove chicken from pan; chop. Add chicken, potato, milk, and 1/4 teaspoon salt to pan; cook for 5 minutes or until thoroughly heated, stirring occasionally. Garnish with parsley, if desired.