Preheat the Oven: Preheat your oven to 375°F (190°C).
Prepare the Peaches: In a mixing bowl, combine the sliced peaches, 1 cup of sugar, cinnamon, nutmeg, and lemon juice. Stir well to coat the peaches evenly, then set aside.
Melt the Butter: Place the butter in a 9x13-inch baking dish and melt it in the preheated oven. Once melted, remove the dish from the oven and set aside.
Make the Batter: In a separate mixing bowl, whisk together the flour, remaining 1 cup of sugar, baking powder, and salt. Gradually add the milk and stir until smooth.
Assemble the Cobbler: Pour the batter over the melted butter in the baking dish, but do not stir. Spoon the peach mixture evenly over the batter.
Bake: Bake in the preheated oven for 40 to 45 minutes, or until the top is golden brown and the edges are bubbling.
Serve: Allow the peach cobbler to cool slightly before serving. Serve warm with a scoop of vanilla ice cream if desired.