Combine yogurt, Dijon mustard, honey, lemon juice, salt, celery seed, and pepper in a medium bowl, whisking to combine. While whisking, slowly drizzle in olive oil until well blended. Set aside or refrigerate up to 3 days.
Combine romaine lettuce, apple, carrot, and celery in a large bowl. Drizzle with desired amount of dressing, tossing to coat. Divide evenly among 4 plates, and top each salad with egg, and walnuts.