Preheat oven to 375°F (190°C). Combine sliced peaches, sugars, lemon juice, cinnamon, and nutmeg in a bowl. Let sit for 10 minutes.

Place butter in a 9×13 inch baking dish and melt it in the oven. Remove once melted.

In a bowl whisk flour, baking powder, salt, and sugar. Add milk and vanilla extract and mix until smooth.

Pour batter over melted butter in the baking dish without stirring.

Spoon the peach mixture evenly over the batter. Do not stir.

Bake for 40 to 45 minutes until the top turns golden brown and the filling bubbles.

Let the cobbler cool for about 10 minutes before serving.