Preheat your oven to 350°F (175°C). Place the butter in a 9x13 inch baking dish and put it in the oven just long enough to melt.
In a medium bowl, whisk together the flour, granulated sugar, baking powder, and salt. Slowly mix in the milk and vanilla extract until a smooth batter forms.
Pour the batter over the melted butter in the baking dish. Do not stir.
In a small bowl, combine the ground cinnamon and light brown sugar and nutmeg. Sprinkle this mixture evenly over the batter. Do not stir.
Carefully pour the hot water/apple cider over the entire mixture without stirring. The water will help create a caramel-like sauce as the cobbler bakes.
Bake in the preheated oven for 40-45 minutes, or until the top is golden brown and the cobbler has set.
Allow the cobbler to cool for at least 15 minutes before serving. This allows the sauce to thicken slightly. Serve warm.