Peach-Blackberry Cobbler

8 to 12 peaches, peeled, pitted, and cut into 1-inch chunks
2 tablespoons cornstarch or flour
5 tablespoons light brown sugar
1 teaspoon freshly squeezed lemon juice
Pinch salt
2 cups blackberries

Topping:
2 cups flour
1/2 teaspoon salt
1/4 cup light brown sugar, packed
2 teaspoons baking powder
1/4 teaspoon dried ginger
1/4 teaspoon cinnamon
2 pinches mace or nutmeg
6 tablespoons (3/4 stick) cold unsalted butter, cut into pieces
3/4 cup plus 1 tablespoon milk
1 tablespoon sugar

Preheat the oven to 350 degrees F. In a bowl, combine the peaches, cornstarch or flour, brown sugar, lemon juice and salt, tossing gently. Carefully fold in the blackberries and transfer the mixture to an 8-cup baking dish. Set aside.
Topping: In a mixer fitted with a paddle attachment (or hand mixer or your fingertips), mix the flour, salt, brown sugar, baking powder, ginger, cinnamon, and mace or nutmeg. Add the butter and mix until coarse and crumbly. Add 3/4 cup of milk and mix just until combined. Turn out the dough onto a lightly floured surface and knead a few times to smooth it out. Form into a ball and roll out into the shape and size of the baking dish, about 1/2-inch thick. Place the dough on top of the prepared fruit.
Brush the top of the dough with the remaining tablespoon of milk and sprinkle with the granulated sugar. Place the cobbler on a sheet-pan to catch any juices that may boil over. Bake until the top is golden brown and juices are bubbling, 25 to 30 minutes. Let cool slightly before serving. Serve warm or at room temperature.