Preheat oven to 425°F (220 degrees C)

In a large bowl, 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, and pour into a 2 quart baking dish. Bake in preheated oven for 10 minutes.

Meanwhile, in a large bowl, combine flour, 1/4 cup brown sugar, baking powder, and salt. Blend in butter with your fingertips, or a pastry blender until mixture resembles a course meal. Stir in water until just combined.

Remove peaches from oven, remove some excess liquid, and drop spoonfuls of topping over them. Sprinkle entire cobbler with the 2 1/2 tablespoons coarse sugar and 1 teaspoon cinnamon.