Place meat in a large resealable bag. In a medium bowl, whisk together the next 5 ingredients (olive oil through salt and pepper). Pour marinade over meat and seal bag.
Refrigerate for at least 2 hours.
In a large crock cooker, place the London broil and the beef broth. Cover and cook on LOW for 6 to 8 hours, until meat is very tender. Allow meat to cool, then slice.
In a medium bowl, toss the beef with the arugula, apple and turnips.
In a small bowl, whisk together the remaining ingredients (lime juice through garlic) with salt and pepper. Pour dressing over salad, toss and serve.