Preheat the oven to 375ºF. Line 8x8 inch pan with parchment paper on the bottom and hanging over the sides of the pan for easy removal after baking.
In a medium size bowl, combine the berries, ⅓ cup sugar, and cornstarch. Stir then set aside.
In a large bowl, stir together flour, ½ cup white sugar, baking powder, and salt.
Use a fork or pastry cutter to cut the butter into flour mixture. Work quickly with the dough until the butter pieces are very small. Note: the dough will be crumbly. You can also pulse in a food processor until you get small sized crumbs.
In a separate small bowl, beat egg and vanilla extract with fork. Add the egg and vanilla to the large bowl and lightly mix until you have a crumbly mixture.
Sprinkle half the dough into the lined pan and press it flat evenly. Then spoon the berry mixture over the bottom crust. Crumble remaining dough over the berry filling layer.
Bake for 45 minutes or until top is light golden brown. Cool completely before cutting into squares, about 2 hours. Make 9 large squares or 16 small.
Refrigerate until ready to serve. Enjoy!