Whisk the sauce ingredients together until combined. Taste, and adjust ingredients if you'd like. Keep in the fridge until ready to use.
For the cakes, briefly pulse the *dry* chickpeas and artichokes in a food processor 5 times, or until the mixture becomes chunky. Think crab cake texture. Spoon the mixture into a large bowl.
Add the chopped bell pepper, celery, green onion, and parsley to the food processor. Pulse until minced. Scrape down the sides of the bowl once or twice between pulsing. Scoop the minced veggies into the chickpea artichoke mixture.
Gently fold in the lemon juice, mayo, mustard, 1 cup of the breadcrumbs, Old Bay, and chickpea flour. Taste the mixture, and adjust seasonings if you wish. (Old Bay is salty enough for me, so I do not add additional salt. Keep in mind the Remoulade has spice and salt as well.)
Form 12 cakes with a 1/4 cup measuring utensil. Gently flatten then coat in remaining breadcrumbs. (You can store prepped, uncooked cakes in the fridge for up to 24 hours if you'd like to cook them later.)
In a large nonstick pan or cast iron, melt the butter or oil over medium heat. Use enough to lightly coat the pan. A well-seasoned cast iron should be nonstick.
Once the butter or oil is hot, carefully place as many cakes as will fit in the hot pan without them touching. Cook until deep golden brown, about 5 minutes per side. If you're making a large batch, you can keep finished cakes warm in a 200°F oven until ready to serve.
Serve with Remoulade and lemon wedges. I used minced bell pepper, green onion, and parsley as garnish.