In a bowl, combine all ingredients except cooking oil and "stuffers"; mix together until well blended. Evenly divide mixture into 6 portions and shape into cakes. Place about 1 TBSP of stuffer in center of each cake and reshape patties to completely cover filling. Flatten cakes slightly.
In a large nonstick skillet, heat oil to medium hot. Place meatcakes in skillet and let brown evenly on all sides. When completely browned, add 1/2 cup water and allow to simmer, covered, until cooked to preferred doneness. Transfer meatcakes to a serving platter and keep warm.
To drippings in skillet, stir in 3-4 TBSP flour and stir constantly until flour browns and skillet looks very dry. Add 1 cup water or beef broth, stirring rapidly and scraping bits of flour loose from pan. Mixture will thicken into a smooth gravy. If too thick, add additional water or broth for desired consistency. Taste for seasoning; if needed, add a little salt. Pour gravy over meatcakes and serve immediately. Makes 6 servings.