Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking pan. In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, and salt until well combined. Cut the cold cubed butter into the dry ingredients with a pastry cutter or fork until the mixture resembles coarse crumbs. Stir in the egg yolk and ice water until a dough forms. Press the dough evenly into the prepared pan and pre-bake for 15-20 minutes until lightly golden.

While the crust is baking, combine the fresh blackberries and granulated sugar in a medium saucepan over medium heat. Cook, stirring gently for 5-7 minutes until the blackberries release their juices and soften. Once softened, stir in the lemon juice and cornstarch, continuing to cook for another 1-2 minutes until the mixture thickens. Remove from heat and let the filling cool slightly before pouring it over the pre-baked crust.

In a separate bowl, whisk together the light brown sugar, baking powder, and flour until uniform. Cut in the cold butter again using a pastry cutter until you achieve a crumbly mixture. Mix in the egg and vanilla extract until just combined, then fold in the shelled pistachios.

Carefully pour the blackberry filling over the pre-baked crust, spreading it out evenly. Next, sprinkle the pistachio topping over the filling, pressing it down gently to ensure it adheres. Place the pan back in the oven and bake for 30-35 minutes, or until the topping is golden brown, and the filling is bubbly and fragrant.

Once baked, remove the pan from the oven and allow the Blackberry Pistachio Dream Bars to cool entirely in the pan for 1-2 hours. When cooled, lift the bars out of the pan using the edges of the parchment paper, and slice into squares or rectangles.