Measure out ¾ cup of the breadcrumbs into a shallow dish and set aside.
In a medium bowl, stir together the mayonnaise, capers, lemon juice, kelp flakes, mustard, Old Bay Seasoning, salt, ground pepper, and cayenne. Add hearts of palm (or jackfruit), bell pepper, celery, parsley, shallots, the remaining ¾ cup of breadcrumbs and stir to combine. Let stand for about 10 minutes to allow the breadcrumbs to bind everything together.
To make the sauce, stir all the ingredients together in a small bowl. Taste and add salt and pepper, if desired. Refrigerate until ready to serve.
Gently shape “crab” cake mixture into small patties, about 3 inches wide and ½ inch thick. Dredge the patties in breadcrumbs. Heat oil in a large skillet over medium heat. Fry cakes until golden brown and crisp, about 3 to 4 minutes per side.
Alternatively, to bake the “crab” cakes, preheat the oven to 375ºF. Line a baking tray with parchment paper. Brush parchment with oil and place shaped cakes on it several inches apart. Bake for about 20 to 25 minutes, carefully flipping once midway through baking.
Serve immediately with a dollop of sauce on top.