Heat up 1 teaspoon of olive oil in a small skillet over medium heat. Cook the onion until softened and translucent, about 5 to 7 minutes. Transfer to a large mixing bowl, and set aside to cool.
To the mixing bowl of cooled onions, add the egg, mayonnaise, mustard, parsley, Old Bay, and salt, and mix until smooth. Fold in the crab meat, being careful not to break up the pieces too much. Add the bread crumbs, and fold the mixture until just combined. Set aside the crab mixture while you prepare the sauce. The moisture in the crab mixture will begin to soften the bread crumbs.
In a small bowl mix together all of the ingredients for the sauce and taste for seasoning. Set aside until you are ready to serve.
Add some bread crumbs to a plate for dredging your crab cakes. Portion out the crab mixture into 8 equal-sized mounds, between ⅓ to ½ cup each. Shape the crab cakes into patties about ¾-inch thick. If the cakes feel a little loose, just gently press them back together with your hands. Dredge each crab cake in bread crumbs and set aside. Refrigerate for up to 1 hour before cooking.
Heat the 1 tablespoon oil in a large nonstick skillet over medium heat. Add the prepared crab cakes and cook for 4 minutes until browned. Add the remaining tablespoon of olive oil before flipping over, and cook the second side for another 4 minutes, or until golden brown. Remove from the heat. Serve immediately accompanied by the sauce.