Preheat your oven to 350°F and position a rack in the middle. Pour the melted butter into a 9x13-inch baking dish, tilting to coat the bottom evenly. This creates the golden crust that makes our peach cobbler cozy homemade so irresistible.
In a medium bowl, combine sliced peaches with granulated sugar, brown sugar, cinnamon, and nutmeg. Toss gently until every peach slice gleams with spice-sweetened coating. Let this sit for five minutes while you prepare the topping.
Whisk together flour, baking powder, and salt in a large mixing bowl. Create a well in the center and add milk and egg. Stir until just combined—overmixing creates tough, dense topping instead of tender cake. I find a fork works best here.
Pour the batter over the buttered baking dish without stirring. It sounds odd, but trust this method—the topping rises up around the filling as it bakes. Arrange prepared peaches and their juices evenly over the batter.
Bake for 35-40 minutes until the topping turns golden brown and springs back when lightly touched. A toothpick inserted into the cake layer should come out clean. The filling will bubble slightly at the edges—this warm peach cobbler is exactly where it needs to be.
Remove from the oven and let cool for 10 minutes before serving. This allows the topping to set slightly while the filling remains warm and inviting. I always use this time to brew fresh coffee or prepare vanilla ice cream.