• Preheat oven to 400° F with a rack in the lower third of the oven.

Make Blackberry Pie Filling

• Place blackberries in a large bowl. Add the sugar, cornstarch, lemon juice and vanilla and stir until well combined. Let the filling mixture rest while you make the pie crust so that the berries release some of their juices.

Make Pie Crust

• Place the flour, granulated sugar and salt in the bowl of a food processor fitted with the steel blade. (Alternatively, the pie dough can be made by hand in a bowl using a pastry cutter.) Pulse a few times to combine.
• Add the cold butter cubes and pulse 10-12 times, until the butter pieces are the size of small peas. Then add the ice-cold water and pulse until the dough starts to come together.
• Turn the dough out onto a lightly floured work surface and bring it together into a ball; cut it in half. Form each half into a round disk. Refrigerate one dough disk.
• Roll out bottom pie crust: On a floured work surface, use a rolling pin to roll the other dough disk out into a circle that is 12 inches in diameter, turning the dough a quarter turn with each roll as you roll it out. Place dough circle into a 9x2-inch deep dish pie dish. (Gently wrap dough around the rolling pin to transfer it.) Gently smooth the dough out into the pie dish, but do not press it down firmly into the dish as this can cause the crust to stick to the dish.

Assemble Pie

• Stir the blackberry mixture again to make sure that everything is well distributed. Transfer the blackberries and all juices from the bowl to the pie dish with the rolled out pie crust. Set aside.
• Roll out the top pie crust: Place the second dough disk onto a floured work surface. Roll it out into a 12-inch diameter circle. To make a lattice top crust, use a sharp knife, pizza cutter or pastry wheel to cut the dough circle into ½-inch strips. Using every other strip from the circle, arrange half of the dough strips going one direction across the top of the pie, leaving a little bit of space in between each strip. Weave the other half of the dough strips through the first set, over and under, pulling back the first set of strips as needed to weave. (As an alternative to the lattice crust, you can place the whole dough round on top of the pie. Cut a few slits in the center to allow steam to escape.)
• Trim the edges of the pie crust so that there is a ½-inch overhang over the edge of the pie dish. Fold the overhang under and use your fingers or a fork to flute/crimp the edges of the crust as desired.

Brush with Egg Wash and Bake

• Egg wash: In a small bowl, beat together the egg and the 1 tablespoon milk. Lightly brush the top of the pie crust with the egg wash. (You will not use all of the egg wash.) If desired, sprinkle coarse sugar or granulated sugar over the top of the pie.
• Bake pie at 400° F for 15 minutes, then reduce the oven temperature to 350° F and continue baking for 45-50 more minutes, until the filling is bubbly and crust is light golden brown. Begin checking on the pie at 30 minutes and cover crust edges with a pie crust shield or foil as needed to prevent over-browning.
• Let pie cool for at least 2-3 hours at room temperature before slicing and serving. Store leftover pie in the refrigerator, wrapped tightly, for up to 5 days.