Make the Tartar Sauce:
Combine vegan mayonnaise, chopped pickle, reserved marinade and dill in a mixing bowl and stir well to combine. Refrigerate until ready to serve.
Make the Cakes:
Pulse chickpeas, hearts of palm, and artichoke hearts in a food processor several times, keeping an eye on the texture. Mixture should be chunky, not minced.
Transfer mixture to a large bowl. Add 1 cup of the bread crumbs, vegan mayonnaise, Dijon mustard, the lemon juice, Old Bay seasoning, seaweed and dill. Taste and add salt and pepper if desired. Mix well. Refrigerate for at least 30 minutes to help the mixture hold together when forming patties.
Once the mixture has cooled, form it into 1 inch thick patties about 2 inches in diameter.
Heat 1 tbsp oil in a non-stick pan. Coat each patty in remaining bread crumbs and fry until golden brown, about 3-5 minutes per side, adding 1 tablespoon of oil per batch of cakes.
Top the cakes with tartar sauce, sprinkle with chopped dill, and serve with a wedge of lemon.