Place the flour, sugar and salt in a food processor. Pulse until well combined. Add the butter and shortening; pulse until mixture resembles a coarse meal. With the motor running, slowly pour in water until dough forms a ball, adding additional 1 to 2 tablespoons more, if needed. Portion into 3 disks and wrap well. Refrigerate for at least 1 hour or up to 2 days.
Preheat oven to 400°F (200°C). Arrange the rack to the lowest position in the oven. Cut 12 parchment paper strips about 1×7-inch (2.5 cm x 18 cm). Line each muffin cup with a strip of parchment (to easily remove pies once baked). Whisk egg with water; set aside.
Roll out two pastry disks on a lightly floured surface to 1/4-inch (5 mm) thick. Cut out 12 (4-inch/10 cm) rounds, rerolling scraps, if needed. Fit rounds into each muffin cup. Fill with 1/4 cup (60 mL) pie filling.
Roll out remaining pastry into a 9-inch square; trim the edges. Cut into 12 portions. Cut each portion into 5 thin strips.
Brush the edge of the pastry in the muffin cups with reserved egg wash. Weave 5 strips over the pie filling to create a lattice top. Seal pastry edges together with fingertips. Brush top with egg wash. Sprinkle with turbinado sugar.
Bake for 25 to 30 minutes or until pastry is golden brown and filling is bubbling. Transfer to a wire rack to cool completely.