Prepare either pie crust recipe through step 5, including chilling for at least 2 hours.

Place ½ cup of each type of berry in a medium bowl and set aside.

Place the remaining 2 and ½ cups blueberries, 1 cup raspberries, and 1 cup blackberries in a medium saucepan over medium heat. Add sugar and cinnamon and cook until berries release some juice.

Combine cornstarch and lemon juice in a small bowl. Remove 3 to 4 Tablespoons of warm berry juice from the saucepan, add to cornstarch bowl, whisk until smooth.

Stir the cornstarch mixture into the saucepan with berries, cook until simmering and thickened, about 5-7 minutes.

Remove from heat and stir in reserved berries, lemon zest, and vanilla. Cool at room temperature for 20 minutes.

Adjust oven rack to lower third position and preheat to 425°F (218°C). Place a baking sheet on the bottom rack.

Roll out one disc of chilled dough to a circle 12 inches in diameter and place it in a 9-inch pie dish.

Spoon the filling into the crust. Roll out the second crust, cut into strips, and arrange in a lattice pattern over the filling.

Brush top and edges with egg wash and sprinkle with coarse sugar, if using.

Bake at 425°F for 20 minutes, then reduce temperature to 375°F (190°C) and bake for 45-55 more minutes.

Remove pie, cool on a rack for at least 5 hours before slicing.