Preheat an oven to 400°F (200°C).
In a 10-inch (25-cm) sauté pan over medium heat, stir together the apples, brown sugar, cornstarch and salt. Sauté until the apples until just tender-crisp, 5 to 7 minutes. Stir in the blackberries and cook until the blackberries soften and begin to release their liquid, 2 to 3 minutes.
Remove from the heat and stir in the vanilla. Set aside and let cool to room temperature.
Roll out the pie dough into a 12-inch (30-cm) round about 1/8 inch (3 mm) thick. Carefully roll the pie dough around your rolling pin and unroll it on top of the pan. Trim the edge, leaving 1 inch (2.5 cm) of overhang, then crimp the edges to seal the dough to the pan.
Brush the edges of the crust with egg wash and sprinkle the top of the pie with the turbinado sugar. Using a small, sharp knife, cut about 5 slits in the crust to allow steam to escape during baking.
Bake until the crust is crisp and golden brown, about 25 minutes. Transfer the pie to a wire rack and let cool for at least 1 hour before serving. Serves 8.