Preheat oven to 350°F.
In a medium pot, combine blackberries, 1 cup sugar, and water. Bring to a boil, reduce heat to a simmer, and cook for 5 to 10 minutes until reduced and thickened, stirring occasionally. Remove from heat.
While blackberries are cooking, whisk together flour, remaining ½ cup sugar, baking powder, and salt in a large bowl. Slowly blend in milk and vanilla and mix until batter is smooth.
Put butter (sliced into 6 equal pieces) in a 9- by 13-inch baking dish and place in preheated oven for a couple of minutes to melt. Remove dish from oven and tilt so that butter evenly coats the bottom. Slowly pour batter over melted butter. Gently spoon berries and syrup evenly over batter without stirring.
Bake for 30 to 35 minutes or until cobbler is light golden brown and tests done with a toothpick inserted in the center. Serve warm with vanilla ice cream or fresh whipped cream.
