For tartar sauce: Combine the artichokes, mayonnaise, cornichons, capers, Dijon and lemon juice in a medium bowl; season with salt and pepper. Refrigerate until ready to use.
For the cakes: In a skillet over medium heat, add 1 tablespoon of the oil and saute the celery, onions and bell peppers until tender, 5 to 6 minutes. Stir in the parsley. Transfer the mixture to a large bowl and add the salmon, cracker crumbs, mayonnaise, Dijon, salt, pepper, egg and lemon zest and juice. Mix with your hands until evenly combined. Shape into patties (I use 1/2 cup per patty, making 8). Place on a baking sheet and refrigerate for 20 minutes.
In a large nonstick skillet, heat 1 tablespoon oil over medium-high heat. Cook the patties (do not overcrowd the pan -- I do 4 at a time) until golden brown, 3 to 4 minutes per side. Add the remaining tablespoon of oil to cook the second batch.
Transfer to a serving platter and serve with the tartar sauce.
These can be made smaller for cocktail party-size portions.