Preheat the oven to 375F. Line an 8x8 baking pan with parchment paper and set aside.
In a bowl, mix flour, 1/4 cup granulated sugar, brown sugar, baking powder, and salt.
Add egg, vanilla extract, and mix well.
Add cold butter cubes into the flour mixture, and mix using a pastry cutter. Continue until all ingredients form together when pressed.
Take 3/4 of the flour mixture and press evenly onto the lined baking pan. This will serve as the bars' base.
In another bowl, mix blackberries, cornstarch, remaining sugar, and lemon juice. Pour blackberry mixture evenly on top of bar base.
Sprinkle with the remaining flour mixture.
Bake for 35-40 minutes and cool slightly before cutting into squares.