1. Preheat oven to 350°.
2. Pour 2 tablespoons melted butter into the bottom of a 2-quart dish coated with cooking spray.
3. Combine peaches, blackberries, and 1 tablespoon flour in a large bowl; toss gently. Add 1/4 cup sugar and ginger; toss gently to combine. Pour peach mixture into prepared baking dish. Lightly spoon remaining 1 cup flour into a dry measuring cup; level with a knife. Combine 1 cup flour, remaining 3/4 cup sugar, baking powder, and salt in a large bowl, stirring with a whisk. Add remaining 2 tablespoons melted butter and milk, stirring with a whisk. Pour batter evenly over fruit mixture.
4. Bake at 350° for 1 hour and 10 minutes or until golden brown.