Place the crabmeat in a large bowl. Carefully pick through the pieces with your fingers. You want to remove any tiny bits of shell. Try not to break up the large lumps too much.

In a small bowl, whisk the melted butter, mayonnaise, and Dijon mustard. Add the parsley, Old Bay, salt, and pepper. Stir until the mixture is smooth and smells very fragrant.

Pour the wet mixture over the crabmeat. Sprinkle the breadcrumbs on top. Use a rubber spatula to fold everything together gently. You want the crab coated but still chunky.

Divide the mixture into four large or eight small patties. Place them on a sheet pan lined with parchment paper. Press them lightly so they hold a nice round shape.

Place the tray in the fridge for at least 30 minutes. This is a vital step. Chilling helps the cakes stay together when you put them in the hot pan later.

Add the vegetable oil to a large skillet over medium heat. Let the oil get hot before adding the cakes. You should hear a gentle sizzle when they touch the pan.

Cook the crab cakes for 4 to 5 minutes on each side. Flip them carefully with a flat spatula. They should be deep golden brown and heated all the way through.

Move the cakes to a plate lined with paper towels. This removes any extra oil. Serve them immediately with fresh lemon wedges and a side of creamy tartar sauce.