In a food processor combine flour butter until incorporated. Add in cold water and continue to blend until it forms a dough. Remove from the food processor and roll into a ball and flatten. Wrap in plastic wrap and refrigerate for 10-15 minutes.
To make the filling:
In a medium sized bowl combine strawberries, blueberries and blackberries with sugar and cornstarch and mix until coated.
Preheat oven to 400 degrees. Roll out the dough into 1/4 inch thickness. Place the filling into the center of the dough. Fold up the edges to seal in the filling. In a small bowl combine the egg and water. Brush the egg wash on the edges and sprinkle with turbinado sugar.
Bake for 35-40 minutes or until golden brown. Remove from oven and let set for 10-15 minutes before serving.