In a mixing bowl, combine the lightly beaten egg, mayonnaise, Dijon mustard, melted butter, chopped fresh parsley, dry mustard, Old Bay seasoning, salt, and pepper. Mix until smooth.

Gently fold in the lump crabmeat, being careful not to overmix.

Shape the crab mixture into 8 equal-sized patties.

Roll each patty in soft breadcrumbs, ensuring they are fully coated.

Heat about 1 inch of oil in a large skillet or frypan over medium-high heat.

Fry the crab cakes in batches, making sure not to overcrowd the pan, until golden brown and crispy on both sides.

Remove the cooked crab cakes and drain on paper towels to remove excess oil.

Keep the cooked crab cakes warm while frying the remaining patties.

Serve the hot crab cakes immediately with lemon wedges and tartar sauce, if desired.