Preheat oven to 375 degrees. Gather the ingredients so that you have everything close at hand on the counter or table.
In a medium bowl, combine the all-purpose flour and salt.
Using a pastry fork, cut in the vegetable shortening until crumbly.
Add cold water in two parts until mixture forms a nice dough. Knead 3-4 times on floured surface. Pat into a ball and flatten.
Assemble the Turnovers
Roll dough out onto a lightly floured surface. Cut out circles using a 5" wide bowl.
Place a generous spoonful of pie filling near center of each circle, about 1/4 cup.
Using your fingertip, spread water around the rim of each. Carefully, fold dough over and crimp with fork.
Place on parchment lined baking sheets and snip a couple of vent holes with scissors or a knife to allow steam to release. Bake in preheated oven for 20-25 minutes until golden brown. Cool on wire racks.
Prepare Icing
In small bowl combine the powdered sugar, whole milk, and vanilla and almond extracts. Mix well.
Drizzle icing over each turnover and allow to set up before serving. Makes 12 turnovers.