In food processor, place chickpeas, hearts of palm, green onion, and jalapeno and pulse to combine and create coarse mixture. Do not blend into purée. Place mixture in large bowl and stir in mayonnaise, Old Bay seasoning, Dijon mustard, and 1 cup panko breadcrumbs. In shallow dish, place remaining 1/2 cup panko breadcrumbs.
Form mixture into 6 equal-sized patties, packing mixture tightly. Turn each patty in shallow bowl of panko crumbs until coated.
In large skillet, heat oil over medium high. Add cakes to skillet and pan-fry for 3 minutes on each side, or until golden and crisp. Do this in two batches, adding more oil to skillet if needed.
To make pesto, in bowl, place dulse, cover with water, and let soak for 10 minutes. Drain rehydrated dulse and place in food processor with basil, sunflower seeds, garlic, lemon juice, and salt. Blend into coarse mixture. With machine running, slowly drizzle olive oil through top feed tube.
Serve crab cakes topped with seaweed pesto.