1. In a large mixing bowl, combine the shredded chicken, breadcrumbs, mayonnaise, Dijon mustard, Old Bay seasoning, lemon juice, beaten egg, and chopped parsley. Mix well.
2. Form the mixture into small patties, about the size of a crab cake.
3. Heat the vegetable oil in a frying pan over medium heat.
4. Fry the chicken cakes in the hot oil until golden brown and crispy, about 3-4 minutes per side.
5. Remove from the pan and drain on paper towels. Serve hot.