In a large bowl gently pick through the lump crab meat to remove any shells and break up large clusters, keeping lumps as intact as possible. Add panko, mayonnaise, egg, Dijon, Worcestershire, Old Bay, chopped parsley, sliced green onion, lemon zest, lemon juice, salt, and black pepper. Fold mixture together carefully with a spatula until combined — do not overmix to preserve lump texture.

Form cakes

Divide mixture into 4 equal portions (about 4 oz each). Using lightly oiled hands, gently shape each portion into a patty roughly 3.5 inches in diameter and about 3/4 inch thick. Place formed patties on a parchment-lined tray and refrigerate for at least 20 minutes to firm up (longer up to 1 hour is fine).

Cook cakes

Heat a large nonstick or cast-iron skillet over medium heat. Add butter and vegetable oil, swirling to coat. When butter foams and begins to brown slightly, add crab cakes leaving space between them. Cook 3–4 minutes per side, gently pressing once with a spatula to ensure even contact, until golden brown and heated through (internal temp ~145°F/63°C). If cakes brown too quickly, lower heat. Transfer to a paper-towel-lined plate and keep warm.

White Tartar Sauce

In a small bowl combine mayonnaise, chopped dill pickle, chopped capers, minced shallot, lemon juice, chopped fresh dill, salt, and pepper. Stir until uniform. Taste and adjust seasoning—add a little more lemon or salt if desired. Refrigerate for at least 15 minutes to let flavors meld.

Creamy Slaw

In a medium bowl toss shredded cabbage and grated carrot. In a small bowl whisk together mayonnaise, apple cider vinegar, sugar, Dijon, salt, and pepper until smooth. Pour dressing over cabbage mixture and toss to coat. Let sit 10–15 minutes to mellow; drain any excess moisture before assembling if needed.

Assembly

Butter the cut sides of buns. Toast buns cut-side down in a skillet over medium heat until golden and crisp, about 1–2 minutes, or toast under a broiler for 1–2 minutes—watch closely.

Spread about 1 tablespoon of white tartar sauce on the bottom half of each toasted bun. Place a lettuce leaf on the sauced bun (if using), then one crab cake. Top the crab cake with about 2–3 tablespoons of creamy slaw, more tartar sauce on the top bun if desired, and close the sandwich.

Serve immediately with lemon wedges on the side for squeezing over the crab cake. Leftover tartar sauce and slaw can be refrigerated for up to 3 days; crab cakes are best eaten the same day.