Lightly grease a 6-quart slow cooker. Combine peaches, orange juice, cornstarch, cinnamon, ginger, nutmeg and 1/4 cup brown sugar in a large bowl. Transfer to the prepared slow cooker.​

Whisk flour, baking powder, salt and the remaining 1/2 cup brown sugar in a medium bowl. Cut cold butter into the flour mixture with a pastry cutter (or 2 knives or your fingers) until the mixture resembles coarse meal. Add milk and stir to combine.​

Dollop large spoonfuls of the batter evenly over the peach mixture. Sprinkle the batter evenly with granulated sugar. Place several layers of paper towels over the slow cooker, allowing 1 to 2 inches to hang over the sides. Place the lid on the slow cooker, securing the paper towels in place. (They will help absorb moisture as the cobbler cooks.) Cook on High until the peaches are tender and syrupy and the topping is caramelized around the edges and cooked through, 2 to 3 hours. Turn off the slow cooker and remove the lid and paper towels. Let cool for 15 minutes before serving. Serve warm.​