Preheat your oven to 350°F (175°C). In a large mixing bowl, whisk together all-purpose flour, granulated sugar, and salt until well combined. Cut in the cold, cubed unsalted butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs. Add the egg yolk and ice water, stirring until a dough forms. Firmly press this dough into a greased 9x13 inch baking pan and pre-bake for 15-20 minutes until lightly golden.

In a medium saucepan over medium heat, combine fresh blackberries and sugar, cooking for about 5-7 minutes until the berries soften and release their juices. Stir in the fresh lemon juice and cornstarch, cooking for an additional 1-2 minutes until the mixture thickens and bubbles. Remove the pan from heat and allow the blackberry filling to cool slightly before spreading it onto the pre-baked crust.

In a clean bowl, whisk together light brown sugar, baking powder, and all-purpose flour until fully blended. Cut in cold butter until the mixture resembles coarse crumbs. Mix in the egg and vanilla extract until just combined, then gently fold in the shelled and unsalted pistachios.

Pour the blackberry filling evenly over the cooled crust, spreading it gently with a spatula. Sprinkle the prepared pistachio topping over the filling and lightly press down to help it adhere. Place the pan in the oven and bake for 30-35 minutes.

Once baked, remove the pan from the oven and let the bars cool completely in the pan on a wire rack for 1-2 hours before slicing.