Unlike a baked peach cobbler or an assembled peach shortcake, this peach dessert is topped with lightly sweetened dumplings and then simmered on the stovetop. The concept is very similar to the way beef or chicken stew with dumplings is prepared except these dumplings are sweet. It's such an easy recipe, you can make it every day during peach season and probably not get tired of it. Use fresh or thawed frozen peaches in the winter and use more or less sugar depending on the tartness of the fruit and to suit your own taste. If desired, toasted chopped pecans can be added to the dumplings for a nutty flavor.