Preheat the oven to 350°F.
Pour melted butter into a 9x9-inch baking dish.
In a medium bowl, mix together flour, 1 cup sugar, the baking powder, cinnamon, nutmeg, and salt. Stir in milk until just combined.
Pour the batter over the melted butter in the baking dish without stirring.
Scatter blackberries evenly over the top of the batter. Sprinkle the remaining 1/3 cup sugar over the blackberries.
Bake in the preheated oven for 55-60 minutes, or until the top is golden brown and a toothpick inserted into the cobbler comes out clean.
Serve warm, ideally with a scoop of vanilla ice cream.