Preheat the oven to 450 degrees F. Butter a 1-quart casserole dish or baking pan.
Combine the sugar with 1 tablespoon of the flour, the berries and 1 cup of water in a medium saucepan. Bring to a boil, reduce the heat and simmer for 2 minutes. 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 of flour until small crumbles start to form. Slowly stir in the milk, adding just enough so a soft dough starts to form and isn't sticking to the sides of the bowl. Once formed, place the dough on a lightly floured cutting board and use your hands to pat it into a square. With a rolling pin, roll the dough to 1/2 inch thick and then cut the dough into 2-inch-wide strips.
Pour 1 cup of the blackberry mixture into the bottom of the buttered dish. Closely line half of the dough strips on top of the blackberry mixture. Bake for 12 minutes or until the dough starts to brown. Remove from the oven and pour the remaining berry mixture over the baked strips. Closely line another layer of dough strips on top and bake for another 12 minutes or until the dough has browned. Serve warm with a scoop of vanilla ice cream.
If self-rising flour isn't available, substitute 2 cups all-purpose flour mixed with 3 teaspoons baking powder and 1/4 teaspoon salt.