Prepare the Mixture: Add the black pepper, salt, and dry mustard into the mixing bowl and mix well.
Add the egg and mayonnaise, mixing well to combine.
Stir in the chopped parsley and crushed saltine crackers.
Gently fold in the crab meat, being careful not to break up the crab too much. Mix until everything is evenly combined.
Shape the crab mixture into patties. This should make about 8-10 patties.
Place each patty on a sheet of waxed paper or parchment paper. Once all patties are formed, cover them with additional waxed paper or plastic wrap.
Refrigerate the patties for at least 1 hour.
Heat a large skillet over medium heat and add the butter and vegetable oil. Allow the butter to melt and the oil to heat up, creating a hot, non-stick surface.
Carefully place the crab cakes into the skillet. Cook for 3 to 5 minutes per side, or until they are golden brown and crispy on the outside.
Once cooked, transfer the crab cakes to a plate lined with paper towels to drain any excess oil.
Serve the crab cakes with warm dipping sauce.
Enjoy!