Combine flours, salt, and sugar in a bowl. Cut in the butter using a pastry cutter, fork, or simply your hands. Mix and crumble together until the mixture resembles coarse meal. Add ice water 1 tablespoon at a time, tossing and stirring with a fork until it just holds together. Wrap in plastic wrap and let rest in fridge at least ½ hour.
Heat oven to 425℉
Make the Filling
Whisk the sugar, cornstarch, and cinnamon together, then add the blueberries and blackberries and toss lightly to combine.
Divide ball of dough in half, and roll out 1 dough disk on floured work surface to about a 11-inch round. Transfer to 9-inch-diameter pie dish (glass or pottery). Trim excess dough, leaving ¾-inch overhang.
Spoon filling into pie crust, discarding the majority of the liquid that has pooled in the bowl.
Roll out the other disc and fit onto the pie dish. Press the edges of the dough together, then crimp with a fork (trim any excess or sort of tuck and press to incorporate into the rest of the dough). Make four slivers in the center of the pie.
Bake the pie in the middle of the oven for 25 minutes. Reduce the temperature to 350°F and bake the pie for 35-45 minutes more, or until the crust is golden and the filling bubbly. Cool on a rack until room temperature before cutting.