Preheat your oven to 375°F (190°C). Lightly grease an 8x8 inch baking dish.

Prepare the filling: In a medium saucepan, combine the drained peaches, reserved syrup, cornstarch, cinnamon, and nutmeg. Heat over medium heat, stirring constantly, until the mixture thickens slightly, about 3-5 minutes. Pour the peach filling into the prepared baking dish.

Prepare the topping: In a separate bowl, whisk together the flour, sugar, baking powder, and salt.

Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs. Stir in the milk until just combined to form a shaggy dough.

Drop spoonfuls of the topping evenly over the peach filling in the baking dish. It does not need to cover the fruit completely; gaps are fine for a cobbler texture.

Bake for 30 to 35 minutes, or until the topping is golden brown and the filling is bubbly. Let cool for at least 15 minutes before serving warm, perhaps with vanilla ice cream.