Preheat the oven to 350°F.
Place the peaches, water, brown sugar and cornstarch in a saucepan. Bring the mixture to a simmer over medium heat, while stirring often. Once the mixture starts to simmer, remove from the heat.
Stir in the lemon juice and butter. Pour into a 9x13-inch baking pan.
In a medium bowl, whisk together the flour, sugar, baking powder and salt. In a small bowl or measuring cup, mix together the milk and melted butter.
Pour the milk mixture into the flour mixture and mix with a rubber spatula until just combined.
Spoon the topping evenly over the peach layer. This works best by placing small dollops of the batter over the filling, then spreading with a small off-set spatula. It is ok if there are a few gaps in the topping but try and make it as even as possible.
In a small bowl, mix together the sugar, nutmeg and cinnamon for the topping. Sprinkle the cinnamon-sugar topping over the cobbler.
Bake for 25-30 minutes, until the top is golden and the fruit is bubbling.
Remove from the oven and let cool for 30 minutes before serving.