In a large bowl, combine the flour and salt. Using a pastry blender, cut in shortening until pieces are the size of small peas. In a small bowl, combine egg, the 1/4 cup cold water and vinegar. Stir egg mixture into flour mixture until all of the dough is moistened. Form dough into a ball. Cover and let rest for 10 minutes. (Dough will be slightly sticky.)
Divide dough in half. Turn one portion dough out onto a well-floured surface. Roll to form a 12x12-inch square. Using pastry wheel or sharp knife, cut into four 6-inch squares.
Peel and core 4 apples. Place an apple on each pastry square. Fold corners to center over apple. Pinch edges to seal. Place dumplings in a greased 15x10x1-inch baking pan. Repeat with remaining pastry and apples.
Bake in a 350 degree F oven for 45 to 50 minutes or until apples are tender and pastry is golden brown. Cool at least 10 minutes.
In a medium saucepan, combine brown sugar, butter, 2/3 cup whipping cream, and corn syrup. Bring to boiling, stirring occasionally; reduce heat to medium. Boil gently, uncovered, for 5 minutes. Remove from heat; stir in vanilla. Transfer to a bowl; cover and set aside to cool slightly. Makes 8 servings.
To serve, in a chilled small bowl, whip 1/3 cup cream to soft peaks. Serve warm dumplings with caramel sauce and whipped cream.