Season the fish fillets with salt and pepper. Poach in simmering water for about 5-6 minutes until just cooked through. Remove, drain well, and flake with a fork, being careful to remove any bones.

In a large bowl, combine the flaked fish, mashed potatoes, parsley, lemon zest, Dijon mustard, and Old Bay seasoning. Mix gently until well incorporated. Taste and adjust seasonings if necessary.

Divide the mixture into 8 equal portions. Shape each portion into a patty about 3 inches in diameter and 3/4 inch thick. Place on a parchment-lined baking sheet.

Refrigerate the patties for at least 30 minutes to firm up. This step is crucial for preventing them from falling apart during cooking.

Beat the egg in a shallow dish. Place the panko breadcrumbs in another dish. Dip each patty into the egg, then coat thoroughly with breadcrumbs.

Heat the vegetable oil in a large skillet over medium heat. Cook the fish cakes for 3-4 minutes per side until golden brown and heated through.

While the fish cakes are cooking, combine all tartar sauce ingredients in a small bowl and mix well. Refrigerate until ready to serve.

Place cooked fish cakes on a paper towel-lined plate to drain any excess oil. Serve warm with the homemade tartar sauce and lemon wedges.