Preheat the oven to 450 degrees F. Butter a 1-quart casserole dish or baking pan. In a medium saucepan, combine the sugar, 1 tablespoon flour, berries and 1 cup water. Bring to a boil, reduce the heat and simmer 2 minutes, then remove from the heat and set aside.
In a medium bowl, use a pastry blender or two knives to cut the butter into the remaining 2 cups flour. Stir in just enough milk to make a soft dough that pulls away from the sides of the bowl. Turn the dough out on a lightly floured board and pat it into a square. Use a rolling pin to roll it to 1/2 inch thick. Cut the dough into 2-inch-wide strips.
Pour 1 cup of the blackberry mixture into the bottom of the prepared pan. Arrange half of the dough strips on top of the berries, placing them close together. Bake until brown, about 12 minutes, then remove from the oven and pour the remaining berry mixture over the baked strips. Arrange another layer of dough strips on top and bake until brown, about 15 minutes. Serve warm with ice cream.