In a large bowl, gently combine the lump crab meat, mayonnaise, beaten egg, Dijon mustard, Worcestershire sauce, Old Bay seasoning, salt, black pepper, and chopped parsley. Mix carefully to avoid breaking up the crab meat.
Add the crushed saltine crackers to the mixture and gently fold until just combined.
Form the mixture into 8 equal-sized patties, about 3 inches in diameter and 1 inch thick. Place the patties on a baking sheet lined with parchment paper.
Refrigerate the crab cakes for at least 15 minutes to help them firm up.
Heat the butter and vegetable oil together in a large skillet over medium heat until the butter is melted and the mixture is hot.
Carefully place the crab cakes in the skillet, cooking in batches if necessary to avoid overcrowding.
Cook the crab cakes for 4 to 5 minutes on each side, or until they are golden brown and crispy.
Remove the crab cakes from the skillet and place them on a paper towel-lined plate to drain any excess oil.
Serve the crab cakes warm with your choice of dipping sauce or lemon wedges.