Combine flour, baking powder and salt. Cut in cold butter pieces until mixture resembles coarse crumbs. Do not over mix.
Combine water and balsamic vinegar and sprinkle over flour mixture. Add only enough to moisten so dough begins to clump. (If necessary add 1 or 2 additional teaspoons of water.)
Form into a 4-5 inch disk, wrap in plastic wrap or place in a gallon sized food storage bag. Refrigerate for 30 minutes before rolling. This will make the dough more elastic and easier to handle.
Roll out dough on a lightly floured surface into slightly larger than 8-inch square (or roll dough in plastic bag and freeze before trimming). Trim to interior dimensions of the top of the baking dish; then cut into 9 smaller squares.
Use a small star shaped canapé cuter or ½-inch apple corer to cut a portion from the center of each square; cut completely through but leave cut pieces in place. Place pastry on small baking sheet or plate and freeze while preparing fruit.
Preheat oven to 375°F. Lightly butter an 8-inch square baking dish.
Rinse and thoroughly drain blackberries and place in a large bowl.
Combine sugar and cinnamon; reserve 1 teaspoon of this mixture and combine the rest with cornstarch.
Add cinnamon sugar/cornstarch mixture to berries and gently stir to coat. Stir in balsamic vinegar and transfer to prepared baking dish.
Arrange pastry squares to cover berries. Trim if necessary – do not overlap. Sprinkle with teaspoon of cinnamon sugar.
Bake 35 minutes or until pastry is golden brown and berry juices begin to bubble. Serve warm.
Rolling dough in a food storage bag eliminates a lot of cleanup and means no further addition of flour. Also, cutting the dough into small squares, makes it easier to handle and will disguise less than perfectly rolled pastry.