Preheat your oven to 375°F (190°C). In a large bowl, combine the sliced peaches, granulated sugar, brown sugar, cinnamon, nutmeg, vanilla extract, and lemon juice. Toss gently to coat the peaches evenly. Let the mixture sit for about 10 minutes to allow the juices to form.

In a separate bowl, whisk together the flour, granulated sugar, brown sugar, baking powder, and salt. Add the cold cubed butter and use a pastry cutter or your fingers to work the butter into the flour mixture until it resembles coarse crumbs.

Pour the peach mixture into a 9x13-inch baking dish. Sprinkle the dough mixture evenly over the top of the peaches. Pour the boiling water over the entire dish, ensuring the dough is moistened.

Place the baking dish in the preheated oven and bake for 40-45 minutes, or until the crust is golden brown and the peaches are bubbly. Allow the cobbler to cool for a few minutes before serving.