Preheat your oven to 375 degrees. Spray a 9x13 inch sheet pan (with rimmed sides) or baking dish with cooking spray and then line with a sheet of parchment paper. Make sure to leave a little extra parchment paper over the sides so it'll be easy to transfer bars for cutting.
In a large mixing bowl mix together flour, 1 cup of sugar, lime zest, baking powder & salt. Using a pastry cutter (or a pastry blended) cut in cold butter pieces until pea sized crumbs form. Add egg into the mixture and use a fork to stir everything together, forming a crumbly mixture. Reserve 1 and 1/2 cups of the dough and refrigerate. Using your hands, press the remaining 3 and 1/2 cups of dough into the bottom of the baking sheet/dish to form a crust.
Bake for 25-30 minutes
While crust is baking, pour cornstarch and remaining 1/3 cup of sugar into a large bowl. Fold in berries, lime juice and vanilla extract. Fold everything together until berries are evenly coated. Pour berry mixture of the baked crust and spread out evenly, covered the whole crust. Sprinkle the reserved 1 and 1/2 cups of remaining dough over the berries.
Bake for 30 minutes, crumble should be golden.
Allow bars to cool completely and then refrigerate overnight. Lift the bars up from the pan using the sides of the parchment paper. Cut into to squares an serve.
**Optional** I drizzled a vanila glaze over the bars before cutting into squares, in a small bowl combine 1/2 cup powdered sugar, 1-2 tablespoons of milk and a splash of vanilla extract, whisk together and drizzle over bars before cutting into squares.