In a small mixing bowl, stir together all the ingredients for the tartar sauce until well combined. Refrigerate until ready to serve the crab cakes.
Drain the marinated artichokes, reserving 2 tablespoons of the liquid to use in the mix. Finely chop the artichoke hearts and add to a large mixing bowl with the remaining ingredients for the crab cakes. Combine well with a fork.
Heat 1 ½ cups of vegetable oil in a large cast iron skillet to 350°F - 360°F.
Set up a dredging station. Add chickpea flour to a wide shallow dish, use another shallow dish for the breadcrumbs, and a bowl for the nondairy milk.
Take ¼ cup of the crabless cake mixture and form a round thick patty with your hands. Place the cake in the chickpea flour and coat all sides evenly. Quickly submerge in nondairy milk and remove it from the liquid, then place in breadcrumbs. Using your hands, cover the crabless cake in breadcrumbs getting all sides well coated then lightly shake off any excess. Batter 2 to 3 at a time right before frying.
Delicately place 2 to 3 cakes in hot oil at once, depending on the size of your pan. Fry for about 4 minutes until golden brown, flipping half way through.
Remove the cakes from the frying pan and place onto a plate covered with paper towel to absorb any excess oil.
Serve immediately with horseradish dill tartar sauce. Leftovers can be heated over medium heat in a pan that’s lightly coated with vegetable oil.