Thinking the term cobbler must have come from the phrase cobbling something together. Whoever cobbled this did a great job!
Preheat oven to 425F.
In a large bowl, combine peaches, sugar, brown sugar, cinnamon, nutmeg, lemon juice, and cornstarch. Toss to coat evenly and pour into a 2-quart baking dish. Bake for 10 minutes.
In a large bowl combine flour, sugar, brown sugar, baking powder and salt. Blend in butter with your fingertips, or pastry blender, until mixture resembles coarse meal. Stir in water until just combined.
Remove peaches from oven and drop spoonfuls of topping over them. Sprinkle entire cobbler with sugar and cinnamon mixture. Bake until topping is golden, about 30 minutes.