Thoroughly mix mayonnaise, egg, parsley, Dijon, lemon juice, Old Bay, Worcestershire, cayenne, salt, and pepper in large bowl.
Gently fold in crab, preserving lumps.
Gently add panko just until combined; mixture should hold as patties.
Form 12 patties about 2 inches across; refrigerate on plate at least 15 minutes to hold together.
Heat butter and oil in large skillet over medium-high. Once butter melts and bubbles, add cakes in uncrowded batches as needed.
Cook 3-4 minutes per side until golden and crisp; transfer to paper-towel-lined plate.
Optionally lightly toast buns. Put cake on each bottom; add lettuce, tomato, and remoulade dollop. Add tops; serve immediately.