Melt the butter over medium heat, stirring constantly until it turns golden brown and develops a nutty aroma. Remove from the heat and allow it to cool slightly.
In a large bowl, combine the sliced peaches with the sugar, lemon juice, cinnamon, and nutmeg. Let the mixture rest for 10 minutes to release its natural juices.
In another bowl, whisk together the flour, baking powder, salt, and remaining sugar.
Add the browned butter, milk, and vanilla extract. Stir until a smooth, thick batter forms.
Preheat the oven to 350°F (175°C). Grease an 8×8-inch baking dish or oven-safe skillet.
Spread the batter evenly into the prepared baking dish.
Spoon the peach mixture and all its juices evenly over the batter without stirring. This simple method helps create the signature layers that make Brown Butter Peach Cobbler so irresistible.
Bake for 40–45 minutes, or until the crust is golden brown and the peaches are bubbling.
Let the cobbler cool for about 10 minutes before serving.
Serve warm with a generous scoop of vanilla ice cream.