Mix together the flour, granulated sugar and salt. Cut the cold butter and chilled vegetable shortening into the flour mixture until incorporated into the dough . Measure out 120 mL (1/2 cup) of water, add ice and stir, then remeasure out 120 mL of the ice water.
Take one tablespoon of ice water and mix it into the flour mixture. Keep doing this until the dough starts to form larger pieces and the water is used up. Fold the dough into two equal sized discs. Refrigerate for two hours.
When the dough has only 10 minutes left to chill, prepare the filling. In a medium-sized bowl, toss together the berries, granulated sugar, balsamic vinegar OR lemon juice and cornstarch. Set aside.
Using a rolling pin, gently roll out the dough, beginning in the center and rolling out in every direction, turning the dough as you go. Roll it into a 12x12 inch circle. Transfer the dough to a baking sheet lined with parchment paper.
Spoon the berry filling into the center of the rolled out dough, then fold up the sides of the dough so that they are partially covering the berries, overlapping the dough where necessary.
Lightly whisk an egg, then use a pastry brush to coat the dough in egg wash. Bake the galette for 40-45 minutes at 375 degrees Fahrenheit, until the berry juices are bubbling and the crust is golden brown. Enjoy!