Gather all ingredients.

To make the tartar sauce: Mix mayonnaise, capers, shallot, parsley, tarragon, horseradish, mustard, and cayenne together in a bowl until well combined. Refrigerate until needed.

Add milk and bay leaf to a saucepan and place the pieces of fish over the top. Season with salt. Bring to a simmer over medium heat, and cook, stirring occasionally, for about 1 minute. As soon as the fish firms up, but before it starts to flake apart, turn off the heat and cover. Let sit for 5 minutes before draining. Let cool, about 10 minutes. Refrigerate until needed.

Meanwhile, bring a pot of lightly salted water to a boil. Add russet potato and boil until tender but not falling apart.

Drain and mash potato in a bowl. Season with salt, black pepper, and cayenne. Add parsley, chives, and lemon zest; add 1 tablespoon tartar sauce mixture. Mix until combined.

Flake chilled fish over the top. Mix until combined.

Scoop out ¼ of the mixture and form into a patty. Repeat with remaining mixture.

Dust cakes with flour on both sides. Brush both sides of cakes with beaten egg. Coat in bread crumbs.

Heat oil in a skillet over medium heat. Pan-fry patties in the hot oil until golden brown and heated through, 3 to 4 minutes per side.

Drain on paper towels.

Serve with tartar sauce and enjoy!