Preheat the oven to 375°F (190°C). In a large bowl, combine peaches, granulated sugar, brown sugar, cinnamon, nutmeg, lemon juice, and cornstarch. Stir gently and set aside.
Place butter in a 9×13-inch baking dish and set it in the oven until fully melted. Remove the dish carefully once melted.
In a medium bowl, whisk together flour, sugar, baking powder, and salt. Slowly add milk, whisking until smooth.
Pour batter evenly over the melted butter without stirring. Spoon the peach mixture evenly over the batter. Do not mix.
Bake for 40–45 minutes until the cobbler is golden brown and set in the center.
Allow the cobbler to cool slightly before serving. Best enjoyed warm.
