Place the turkey breast in the bottom of the slow cooker.
In a small bowl, stir together the lemon juice, lemon zest, minced garlic, olive oil, thyme, rosemary, salt, and pepper.
Pour the lemon herb mixture over the turkey, turning the meat once so it is coated on all sides.
Pour the chicken broth around the turkey, not directly on top, to keep the seasoning in place.
Arrange the trimmed green beans around the turkey in an even layer.
Cover and cook on low for 6 hours, until the turkey reaches an internal temperature of 165°F.
Remove the turkey, let it rest for 5 minutes, then slice it. Sprinkle the fresh parsley over the turkey and green beans before serving.