Preheat oven to 425 degrees. In a large bowl, combine sliced peaches, 1/4 cup white sugar, 1/4 cup brown sugar, 1/2 teaspoon cinnamon, nutmeg, lemon juice, vanilla or almond extract, and cornstarch.
Toss to coat peaches evenly and pour into a 2-quart baking dish or 5-6 individual baking dishes. Bake in preheated oven for 10 minutes.
Meanwhile, in a medium bowl, combine flour, 1/4 cup white sugar, 1/4 cup brown sugar, baking powder, and salt. Blend in butter with a pastry cutter or your fingertips until mixture resembles coarse meal. Stir in boiling water until just combined.
In a small bowl, stir together the 3 tablespoons of white sugar with 1 teaspoon of cinnamon.
Remove peaches from oven, and drop spoonfuls of topping over them. Sprinkle the cinnamon and sugar mixture evenly over the topping. Bake for 25-35 minutes, or until topping is golden brown. Serve warm with vanilla ice cream.