Preheat the oven to 400°F / 204°C.
Line a baking pan with aluminum foil to catch any filling that may bubble over during baking.
Lightly sprinkle flour over the pie plate.
Place the bottom pie crust into the prepared pie plate.
Gently press the crust into the plate without stretching it.
Trim any excess crust from the edges, if necessary.
In a large saucepan, combine the blackberries, raspberries, and sugar.
Place the saucepan over medium heat.
Cook the berry mixture for approximately 5 minutes, stirring regularly, until the sugar dissolves and the berries begin to release their juices.
Taste the berry mixture carefully.
If additional sweetness is desired, add more sugar 1 tablespoon at a time, stirring after each addition.
In a separate small bowl, combine the lemon juice and cornstarch.
Mix until a smooth slurry forms.
Gradually pour the lemon juice and cornstarch slurry into the simmering berry mixture while stirring continuously.
Continue cooking and stirring for 2 to 3 minutes, or until the filling thickens slightly.
Remove the saucepan from the heat.
Allow the berry filling to cool for approximately 10 minutes before assembling the pie.
Pour the slightly cooled berry filling into the prepared bottom crust.
Spread the filling evenly inside the crust.
Place the top pie crust over the berry filling.
Seal the edges of the top and bottom crusts together by crimping with a fork or with your fingers.
Cut several small slits in the top crust to allow steam to escape during baking.
Brush the top crust evenly with milk.
Sprinkle the coarse sugar over the brushed crust.
Place the pie on the prepared foil-lined baking pan.
Bake at 400°F / 204°C for 40 to 45 minutes, or until the crust is golden brown and the filling bubbles through the slits.
If the crust edges begin to brown too quickly, cover them with foil strips or a pie crust shield halfway through baking.
Remove the pie from the oven.
Place the pie on a cooling rack.
Allow the pie to cool at room temperature for approximately 2 hours.
Transfer the pie to the refrigerator.
Chill thoroughly for approximately 3 hours before serving.
Slice and serve once the filling has fully set.