To make the dough combine the flour, sugar and salt in the bowl of a food processor. Add the butter and shortening and pulse until the mixture resembles a coarse meal. Add the cold water and pulse just until the dough starts to hold together. Don't over process.
Gather the dough together and divide in half. Form each half into a disc. Wrap each tightly with plastic wrap and refrigerate at least 30 minutes or overnight.
To make the filling combine the cornstarch and 1 tablespoon cold water in a small sauce pan. Whisk until smooth. Add the jam and heat over medium until it comes to a boil. Simmer stirring constantly for 2 minutes. Remove from the heat and allow it to cool until ready to use.
Remove the dough from the refrigerator and allow it to rest 10-15 minutes. Lightly flour a clean work surface and dust the dough with flour. Roll the dough to about ⅛" thick large enough to cut into a 9" x 12" rectangle. Cut the 9x12 inch rectangle into 9 equal 3x4" pieces by cutting four lines across on the 12-inch side and three down the 9-inch side. Gather dough scraps together and set aside.
Place the 9 individual pieces of dough on a parchment lined baking sheet.
Beat together the egg and milk. Brush the egg mixture all over the cut pastry pieces. Place 1 tablespoon of the filling in the center of each pastry.
Roll out the second pastry disc to the same dimensions and cut into 9 individual pieces. Prick the dough with the tines of a fork, the round end of a small clean paint brush or chop stick to create vent holes.
Place each piece of vented dough over the filling. Press the edges together firmly with a fork to seal. Repeat until all pockets are formed.
Brush the tops of the pockets with a little bit of the egg and milk mixture. Place the baking sheet with the uncovered pastries in the refrigerator for 30 minutes.
Preheat oven to 350°F.
Gather all remaining scraps of dough and divide in half. Roll out to 1/8" thick and cut into additional 3x4" pieces or use a biscuit cutter to make round pieces. Repeat with remaining dough by filling, brushing and refrigerating. I was able to make 6 additional small round pie pockets with the ingredients at hand.
Remove the pastries from the refrigerator and bake at 350°F for 30 minutes or until golden brown.
Remove the pastries to a wire rack and cool.