Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish and set it aside.

In a large mixing bowl, combine the sliced peaches, 1/4 cup granulated sugar, 1/4 cup brown sugar, cinnamon, nutmeg, vanilla extract, lemon juice, and cornstarch. Stir until the peaches are evenly coated with the mixture.

Pour the peach mixture into the prepared baking dish, spreading it out evenly.

In another mixing bowl, whisk together the flour, 3/4 cup granulated sugar, baking powder, and salt.

Cut the chilled butter into the dry mixture using a pastry cutter or your fingers until the mixture resembles coarse crumbs.

Gradually stir in the boiling water until the topping forms a soft dough.

Drop spoonfuls of the dough over the peach mixture, covering most of the surface but leaving some gaps for steam to escape.

Sprinkle 1 tablespoon of granulated sugar evenly over the dough for added sweetness and texture.

Bake in the preheated oven for 40-45 minutes, or until the topping is golden brown and the peaches are bubbling.

Remove the cobbler from the oven and let it cool slightly before serving. Serve warm with a scoop of vanilla ice cream or whipped cream, if desired.