Preheat oven to 375°F (190°C).
Place sliced peaches in an 8x8 baking dish.
Mix 1/2 cup brown sugar with peaches.
In a large mixing bowl, combine 1 cup all-purpose flour and 8 tbsp cold butter until mixture resembles coarse crumbs.
Add 1 tsp baking powder, 1/2 tsp baking soda, and 1/4 tsp salt; mix well.
Stir in 1 cup active sourdough starter, 3/4 cup milk, and 1/2 cup white sugar until dough is smooth.
Spoon cobbler dough over peaches, spreading evenly.
Pour 4 tbsp melted butter over the dough.
Sprinkle 1/4 cup brown sugar over the melted butter.
Bake in preheated oven for 35-45 minutes, until top is golden brown and dough is cooked through.
Cool slightly before serving.
Serve warm with a scoop of vanilla ice cream for an extra delicious treat.
