Preheat your oven to 425 degrees F (220 degrees C).
In a large bowl, combine the peaches, ¼ cup white sugar, ¼ cup brown sugar, ¼ teaspoon ground cinnamon, nutmeg, lemon juice, and cornstarch. Toss to coat evenly, and pour into a 2-quart baking dish. Bake in preheated oven for 10 minutes.
In another large bowl, combine the flour, ¼ cup white sugar, ¼ cup brown sugar, baking powder, and salt. Blend in the chilled butter with your fingertips or a pastry blender until the mixture resembles coarse meal. Stir in the boiling water until just combined.
Remove the peaches from the oven and drop spoonfuls of the topping over them.
In a small bowl, mix 3 tablespoons white sugar and 1 teaspoon ground cinnamon together. Sprinkle over the entire cobbler.
Bake in the preheated oven until the topping is golden and crisp, about 30 minutes.