Place picked over crab in a mixing bowl. Refrigerate. Mix egg and mayonnaise together. Add all additional ingredients you want to include. Mix and pour over crab meat. Gently fold ingredients together. Let the mixture rest in the refrigerator for at least 10 minutes.
Sprinkle additional breadcrumbs on a plate. Divide the crab mixture into equal parts. Gently form a loose ball from each part and press into breadcrumbs to form a disheveled patty. When all patties are formed, cover and refrigerate until ready to cook.
In a skillet over medium heat warm about 1/2 inch of neutral oil. Flavorless with a high smoking point, such as canola or even butter. Carefully add crab cakes and turn when nicely colored, abut 3 or 4 minutes. Flip and cook second side the same, about 2 minutes. Serve immediately.