In a large bowl, mix together flour, sugar, and salt. Using a pastry blender or 2 knives, cut shortening and butter into flour mixture until coarse crumbs form.
Stir in water, 1 tablespoon at a time, tossing with a fork until a soft dough forms. Shape into a disk, wrap in plastic wrap, and chill for 1 hour.
To prepare filling, dissolve cornstarch in water.
In a medium saucepan, heat blackberries, sugar and cinnamon over medium heat, stirring occasionally, until mixture boils. Add cornstarch mixture, stirring constantly until thickened. Remove from heat. Cool completely.
Preheat oven to 400 degrees. Grease a baking sheet.
On a floured surface, using a floured rolling pin, roll dough to a 1/8" thickness. Cut out six 6" circles. Gather trimmings, roll to a 1/8" thickness, and cut out pastry leaves.
Spoon filling evenly into center of each circle. Fold dough over filling. Press edges to seal.
Place turnovers on prepared baking sheet. Brush with some beaten egg. Place pastry leaves on top of turnovers. Brush iwth remaining egg.
Bake turnovers until golden, 30 minutes. Transfer baking sheet to a wire rack to cool. Garnish with blackberries and mint sprigs.