Preheat the oven to 350°F and grease a 9x13-inch or similar baking dish.

In a large bowl, toss the peaches with the brown sugar, lemon juice, cornstarch, cinnamon, and nutmeg. Spread evenly at the bottom of the prepared baking dish.

Make the topping: In a large bowl, whisk together the flour, sugar, baking powder, and salt. Add the butter and toss to coat. Use your hands or a pastry cutter to work the butter into the dry ingredients until the mixture resembles a coarse meal.

Add the milk and mix with a spatula until a shaggy dough forms. Add more as needed, 1 tablespoon at a time, to moisten any remaining dry flour and bring the mixture together into a soft, cohesive dough. I typically use 2 more tablespoons. Add just enough to bring the dough together, kneading with your hands if necessary.

Tear the dough into golfball-sized pieces and use your hands to flatten them until they're about 1/3-inch thick. Lay them over the peaches in the baking dish. The topping won’t cover all the peaches, so space the biscuits evenly over them, leaving some gaps in between.

In a small bowl, stir together the 1 tablespoon sugar and the cinnamon. Brush the tops of the biscuits with milk and sprinkle the cinnamon sugar over the cobbler.

Bake for 45 to 55 minutes, or until the peaches are bubbling and the biscuits are golden brown on top. A toothpick inserted into the biscuits should come out clean.

Let cool for 10 minutes before serving with vanilla ice cream.