In a medium bowl, whisk together the egg, mayonnaise, Dijon mustard, Worcestershire sauce, lemon juice, Old Bay Seasoning and 1/2 teaspoon kosher salt.
Stir in the crab meat, celery and breadcrumbs.
Line a baking sheet with parchment paper or foil.
Scoop out 1/2-cup portions of the crab mixture and lightly shape it into cakes that are barely flattened. (They should be tall and thick rather than thin and flat.) Cover and refrigerate the crab cakes for a minimum of 1 hour and up to overnight.
When ready to cook, place a large skillet over medium heat and coat generously with oil.
Once the oil is hot, add several crab cakes and cook, flipping once, until golden brown, 4 to 5 minutes per side. Remove the crab cakes from the skillet and serve warm.