Preheat oven to 375° degrees F. Line a 9x13 light metal rectangular baking pan with foil, extending the foil over the edges of the pan. Spray with cooking spray; set aside.
For the crust: In a large bowl, combine the sugar, baking powder, salt, and flour and mix well. Add in the cubed butter, lightly beaten egg and vanilla extract and mix together using a pastry cutter or two forks, mixing until mixture resembles small pebbles. Dough will be crumbly.
Press half of the dough into the prepared pan, using your hands to compress it into a nice, even layer. Set aside briefly.
Meanwhile, for the filling: In a medium bowl, combine the blackberries, granulated sugar, cornstarch, and lime juice & zest with a spoon until combined. Pour the mixture evenly over the crust in the pan. Crumble the remaining crust mixture evenly over the surface of the blackberry layer.
Bake for 38-45 minutes or until the mixture is light golden brown and bubbly and center appears set. Cool completely for at least 1-2 hours at room temperature before cutting into bars, or you may refrigerate.