Put the crab in a medium bowl. In a small bowl, whisk the egg, mayonnaise, mustard, Old Bay seasoning, lemon juice, Worcestershire sauce, and ¼ tsp. salt. Scrape the mixture over the crab and mix gently until well combined. Gently break up the lumps, but do not overmix.
Add the breadcrumbs and parsley and mix them in thoroughly but gently, the mixture should still be somewhat loose. Cover with plastic wrap and refrigerate for 1 to 3 hours.
Shape the crab mixture into 8 cakes about 1-inch-thick.
In a Large (12-inch) nonstick skillet, heat the butter with the olive oil over medium heat. When the butter is frothy, add the cakes to the pan. Cook until dark golden brown on the underside, about 4 minutes. Flip the cakes, reduce the heat to medium low, and continue cooking until the other side is well browned, 4 to 5 minutes.
Serve with lemon wedges on the side for squeezing over the cakes.