Preheat the oven to 425°F (220°C). Lightly grease a 2-quart baking dish.
Place the sliced peaches in a large bowl. Add 1/4 cup granulated sugar, 1/4 cup brown sugar, 1/4 teaspoon cinnamon, nutmeg, lemon juice, and cornstarch.
Gently toss until the peaches are evenly coated. Transfer the peach mixture and its juices to the prepared baking dish.
Bake the peaches for 10 minutes. This gives the fruit a head start and begins creating the syrupy cobbler filling.
While the peaches bake, combine the flour, 1/4 cup granulated sugar, 1/4 cup brown sugar, baking powder, and salt in a mixing bowl.
Add the cold cubed butter. Use a pastry blender or your fingertips to work the butter into the dry ingredients until the mixture resembles coarse crumbs.
Pour in the boiling water and stir gently until a soft dough forms. Avoid overmixing.
Carefully remove the hot peaches from the oven. Drop spoonfuls of cobbler dough evenly over the fruit, leaving a few small spaces for the peach filling to bubble through.
In a small bowl, combine the remaining 3 tablespoons granulated sugar with 1 teaspoon cinnamon.
Sprinkle the cinnamon-sugar mixture evenly over the topping.
Return the Fresh Southern Peach Cobbler to the oven and bake for approximately 30 minutes, or until the topping is deeply golden and the peach filling is bubbling around the edges.
Let the cobbler rest for about 10–15 minutes before serving so the hot filling can thicken slightly.