Prepare a breading station with three shallow bowls: one with flour, one with beaten eggs mixed with milk, and one with panko breadcrumbs seasoned with salt and pepper. Dip each fish fillet first into the flour, shaking off excess, then into the egg mixture, and finally coat thoroughly with panko. Place coated fillets on a plate.
Heat enough oil in a deep fryer or large skillet to fully submerge the fish, heating to 350°F (175°C). Carefully add the breaded fillets into the hot oil, frying in batches if necessary. Cook for about 3-4 minutes per side until golden brown and crispy, then remove with tongs and drain on paper towels.
While the fish is cooking, toast the hamburger buns until lightly golden and crisp. Spread tartar sauce on the bottom bun if desired. Place a crispy fish fillet on each bottom bun.
Add optional toppings such as lettuce leaves on top of the fish. Cover with the top bun. Serve immediately, with extra tartar sauce on the side if preferred.
