Melt ¼ cup butter in a skillet and add the onion and celery. Sauté until tender and spoon into a bowl. Stir in the shrimp and 1/3 cup breadcrumbs into the onion mixture. Mix the mayonnaise, parsley, Old Bay seasoning, Worcestershire sauce, Tabasco sauce, salt and pepper in a bowl and stir into shrimp mixture.
Shape the shrimp mixture into 8 cakes and arrange in a single layer on a baking sheet lined with wax paper. Chill, covered with plastic wrap, for 1 to 4 hours.
Coat the cakes with 1/3 cup bread crumbs. Melt 2 tablespoons butter in a heavy skillet over medium heat and add the cakes. Cook for 2 to 3 minutes per side or until golden brown. Serve the cakes warm with lemon wedges or Lemon Butter Sauce.
Lemon Butter Sauce
Sauté 2 minced garlic cloves in ½ cup butter in a small saucepan for 1 minute. Whisk in 1½ tablespoons cornstarch until combined. Stir in ½ cup dry white wine and bring to a boil. Cook for 1 minute or until thickened, stirring constantly. Remove from heat and stir in 1 tablespoon fresh lemon juice, 3 chopped green onions, ½ teaspoon salt and ¼ teaspoon ground red pepper.