Preheat the oven to 450°. Grease an 8-inch square baking dish.
In a medium saucepan, combine the sugar, 1 tablespoon flour, the berries and 1 cup water (if you use frozen blueberries, add 1 tablespoon fresh lemon juice to the simmered filling). Bring to a boil, lower the heat and simmer for 2 minutes; remove from the heat.
In a medium bowl, rub the butter into the remaining 2 cups flour. Stir in the milk until a soft dough forms.
Turn out the dough on a lightly floured surface. Pat into a square, then roll into an 8-inch square; cut into 6 long strips.
Pour 1 cup of the berry mixture into the pan. Arrange 3 dough strips an equal distance apart over the blackberry mix.
Bake until golden-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 perpendicular to the first row and bake until golden-brown, about 12 minutes more.
Let cool for about 20 minutes.
Serve warm with the ice cream.