Blend flour and salt in medium mixing bowl. Cut chilled shortening into 1/2-inch cubes. Cut in chilled shortening cubes into flour mixture, using a pastry blender, in an up and down chopping motion, until mixture resembles coarse crumbs with some small pea-sized pieces remaining.
Sprinkle half the maximum recommended amount of ice cold water over the flour mixture. Using a fork, stir and draw flour from bottom of bowl to the top, distributing moisture evenly into flour. Press chunks down to bottom of bowl with fork. Add more water by the tablespoon, until dough is moist enough to hold together when pressed together.
To test the dough for proper moistness by squeezing a marble-sized ball of dough in your hand. If it holds together firmly, do not add any additional water. If the dough crumbles, add more water by the tablespoonful, until dough is moist enough to form a smooth ball when pressed together.
Shape the dough into a ball. For ease in rolling, wrap dough in plastic wrap. Chill for 30 minutes or up to 2 days.
FOR THE FILLING:
Combine apples and water in small saucepan. Cook and stir on high heat until mixture comes to a boil. Reduce heat to low. Simmer 5 minutes. Stir in brown sugar, cinnamon and nutmeg. Simmer 5 minutes.; stir frequently. Combine flour and granulated sugar. Stir into apple mixture. Bring to a boil. Boil 1 minute. Stir in butter.
Heat oven to 425ºF. Roll out refrigerated pie dough. Cut six 5 1/4-inch circles from each half (reroll circles as necessary to 1/16-inch thickness).
Place about 1 tablespoon apple filling on each dough circle. Moisten edges with water. Fold in half over filling. Press with fork to seal. Place on ungreased baking sheet. Prick tops with fork to let steam escape.
Bake 20 minutes or until golden brown. Cool 10 minutes on wire rack.
Combine powdered sugar, milk and vanilla in small bowl. Stir well. Drizzle over turnovers. Serve warm or cool.
Note: Any canned fruit pie filling can be substituted for fresh apple filling.