Preheat the oven to 400 degrees F.
For the crust: In a food processor, add the flour and a nice pinch of salt. Pulse very lightly just to blend. Add the butter evenly around the flour and quickly pulse until the flour resembles small crumbles. Slowly pour the water through the spout until the dough begins to come together. Remove and quickly form into a disc. Tightly cover with plastic wrap. Refrigerate for 20 minutes.
Meanwhile, for the filling: In a large bowl, add the blueberries, apples, sugar, cornstarch, cinnamon, lemon juice and a pinch of salt. Stir to combine and set aside.
Remove the dough from the refrigerator and place on a lightly floured surface. Gently roll the disc into a circle big enough to fit into the pie pan and leave a 3-inch overhang. The dough should be about 1/8-inch thick. Using a pizza cutter, trim the edges of the dough. Place the dough into the pie pan and press gently against the bottom and sides to fit the dough into the pan. Pour in the fruit filling, and then scatter the butter evenly around the top of the pie. Fold the extra dough that's hanging off the edge over the top to create the top of the pie crust. Leave a hole in the center for ventilation.
Whisk the egg with 1 teaspoon water and brush the top with egg wash and then sprinkle with the sugar.
Place in the oven and bake until the crust is golden brown, about 35 minutes. Let the pie rest at least an hour before serving to let the filling set.