Soak hearts of palm in water for 30 minutes. Drain well.
Chop hearts of palm into lobster-like chunks.
Add hearts of palm to medium bowl with remainder of ingredients. Stir well to coat and combine.
For best results, let mixture marinate in the fridge for a couple hours.
Scoop some "lobster" salad into one of the rolls, top with celery leaves if desired. Add a final sprinkle of Old Bay on top and serve.