In a large nonstick pan over medium-high heat, heat the oil. Add the corn, onion, and red pepper and cook until just tender, 5 minutes. Transfer the mixture to a food processor and pulse to form a coarse puree.
In a large bowl, add the corn mixture, shredded hearts of palm. breadcrumbs, mayonnaise, nori, parsley, Old Bay, mustard powder, salt, and pepper. Stir gently to combine.
On a large plate, place a generous layer of breadcrumbs. Line another plate or baking sheet with parchment. Using a ¼-cup measure, scoop out portions of the crab cake mixture, flatten slightly with your hands, and dredge in the breadcrumbs. Place on the parchment-lined plate and repeat with the remaining mixture.
In a large, deep nonstick or cast-iron pan over medium-high heat, add a thin layer of oil. When the oil is shimmering, working in batches if needed, fry the crab cakes until golden, about 2 minutes per side. Transfer to a plate and repeat with the remaining crab cakes.