Preheat the oven to 375 degrees F. Either grease or spray with baking spray an 8x8 inch pan or place parchment paper on the bottom of the pan.
In a medium bowl, stir together white and brown sugar, flour, baking powder and salt.
In a measuring cup or small bowl, beat an egg with a fork. Add the egg and vanilla to the flour mixture. Using a fork or a pastry cutter, cut in the butter into the flour mixture. Work with the dough until the pieces are very small. Dough will be crumbly. Pat half of the dough evenly into the bottom of the prepared pan.
In another bowl, stir together the sugar, cornstarch, and lemon juice. Stir in the blueberries. Spoon the blueberry mixture evenly over the bottom crust.
Crumble the remaining dough over the blueberry layer.
Bake in a preheated oven for 45 minutes, or until top is slightly brown. (My oven runs hot and baked in about 38 minutes.)
Cool completely before cutting into squares. I recommend refrigerating until ready to serve.