In a bowl, combine the four and salt, cut in shortening until crumbly. Gradually add water, tossing with a fork until dough forms a ball. On a lightly floured surface, roll out dough to a12 X 18 rectangle. Cut into six squares.
Place 1/3 cup chopped apples in the center of each square. Brush edges of dough with water, fold up corners to center and pinch to seal. Place in a greased 13X9X2 baking dish. Bake at 350 degrees for 30 minutes.
In a saucepan, combine the brown sugar, water and butter, bring to a boil, stirring constantly. Removing from the heat. Pour over dumplings. Bake 25-30 minutes longer or until apples are tender. Serve warm ice cream.