In a 2 quart baking dish, combine peaches, 1/4 cup white sugar, 1/4 cup brown sugar, 1/4 teaspoon cinnamon, nutmeg, lemon juice, and cornstarch. Toss to coat evenly. Set aside.
Meanwhile, in a med bowl, combine flour, 1/4 cup white sugar, 1/4 cup brown sugar, baking powder, and salt. Blend in butter with your fingertips, or a pastry blender, until mixture resembles coarse meal. Stir in water until just combined.
Stir peach mixture and then drop flour mixture by spoonfuls over the peaches. Sprinkle entire cobbler with the sugar and cinnamon mixture. Bake until topping is golden, about 30-45 minutes.