Brown the Butter
Melt the butter in a medium saucepan over medium heat. Stir constantly as it foams and gradually turns golden brown with a rich, nutty aroma. Remove from the heat immediately and let it cool slightly.
Prepare the Peaches
Combine the sliced peaches with the sugar, lemon juice, cinnamon, and nutmeg in a large bowl. Allow the mixture to rest for about 10 minutes so the peaches release their natural juices.
Make the Batter
In another bowl, whisk together the flour, baking powder, salt, and the remaining sugar. Stir in the cooled brown butter, milk, and vanilla extract until a smooth batter forms.
Assemble
Preheat the oven to 350°F (175°C).
Grease an 8×8-inch baking dish or oven-safe skillet. Pour the batter into the dish and spread evenly. Spoon the peach mixture and all of its juices over the batter without stirring. This classic layering creates the signature texture of Brown Butter Peach Cobbler.
Bake
Bake for 40–45 minutes until the crust is golden brown and the peach filling is bubbling around the edges. If the crust browns too quickly, loosely cover with foil.
Cool and Serve
Let the cobbler cool for about 10 minutes before serving. Enjoy warm with plenty of vanilla ice cream.