Preheat the oven to 350°F (175°C). Grease or line an 8×8-inch baking pan.

Make the crust: pulse flour, 1/2 cup cold cubed butter, 1/4 cup granulated sugar, and salt in a food processor until coarse crumbs form. Add the egg yolk and 2 tablespoons ice water; pulse until the dough just comes together, adding up to 2 more tablespoons if needed. Press half the dough evenly into the bottom of the pan.

Blind-bake the base for 10–12 minutes until set but not fully browned; remove from oven.

Prepare the filling: in a saucepan, combine the blackberries, 1/2 cup granulated sugar, lemon juice, and cornstarch. Cook over medium heat, stirring, until the berries release juice and the mixture thickens and becomes glossy, about 6–8 minutes. Taste and adjust sugar as needed. Remove from heat.

Spread the warm blackberry filling evenly over the par-baked crust.

Make the pistachio crumble: pulse pistachios, 1/2 cup cold cubed butter, 1/2 cup light brown sugar, baking powder, 1 large egg, and vanilla extract in a food processor until coarse and clumpy; crumble this mixture over the blackberry layer.

Bake the assembled bars for 20–25 minutes, until the topping is golden and set. Let cool completely in the pan on a rack before chilling for at least 1 hour to set.

Lift from the pan, slice into bars, and serve.