Melt the butter in a small saute pan over medium-high heat. Add the onions, celery, and bell peppers. Cook, stirring, until the vegetables are soft and slightly golden, 2 to 3 minutes. Add the garlic, 1/4 teaspoon of the salt, and the cayenne. Cook for 1 minute longer. Remove the pan from the heat and cool for 5 minutes.
In a large mixing bowl, combine the shredded chicken, cooled vegetables, green onions, 1/2 cup of the bread crumbs, mayonnaise, eggs, and Creole mustard. Season mixture with the remaining 1/2 teaspoon of the salt and the pepper and mix well. Divide the mixture into 12 equal portions, about 1/4 cup each, and form them into round 1/2-inch thick cakes or patties.
Place the remaining 1/4 cup of bread crumbs in a shallow dish and dredge each cake in the bread crumbs, pressing gently to coat. Place cakes on a parchment-lined baking sheet and refrigerate for 30 minutes.
In a large saute pan with high sides heat the vegetable oil to 360 degrees F. Gently lay the chilled cakes in the oil, 3 to 4 at a time, and fry until lightly golden, 1 to 2 minutes on each side. Remove cakes with a slotted spatula and drain on paper towels. Serve hot with the Tangy Remoulade Sauce.
Yield: 12 appetizer servings