Check the crab meat for any hard or sharp pieces and discard them.
In a large bowl, whisk together the mayonnaise, egg, Dijon mustard, Worcestershire sauce, lemon juice, Old Bay seasoning, 1/2 teaspoon salt, and 1/4 teaspoon black pepper.
Add the crabmeat, breadcrumbs, and parsley and mix gently to combine, being careful not to break up the crab.
Using about 1/3 cup per crab cake, gently shape the mixture into 6 crab cakes (or use about 1/4 cup and make 8 smaller crab cakes), each about 1-inch-thick. Transfer the crab cakes to a plate, cover with plastic, and refrigerate for at least 1 hour (and up to 24 hours). Chilling gives the panko a chance to absorb the other ingredients which ensures the crab cakes don't fall apart.
Preheat the oven to 425 degrees. Line a large baking sheet with parchment paper or coat with cooking spray.
Transfer the crab cakes to the prepared pan and brush the top and sides with olive oil.
Bake for 15 to 18 minutes until browned and cooked through (165 degrees on a meat thermometer).
To pan fry these crab cakes, heat about 1/4 cup of vegetable oil or olive oil in a high-sided skillet over medium heat. Working in batches to prevent crowding the pan, add the crab cakes to the hot oil and cook for 3 to 5 minutes per side, until golden brown and cooked through. The internal temperature should reach 165 degrees on a meat thermometer.