Preheat the oven to 450 degrees F (230 degrees C).

Combine blackberries, peaches, sugar, and cornstarch in a large bowl.

Press one pie crust into the bottom of a 9-inch pie pan. Pour blackberry mixture into crust; cover with remaining pie crust. Press edges together to seal. Cut slits in the top of the pie to vent. Brush top with melted butter; sprinkle cinnamon and nutmeg on top.

Bake in the preheated oven for 15 minutes. Reduce the temperature to 350 degrees F (175 degrees C): continue to cook until the top crust is golden brown, 35 to 40 minutes.