Preheat oven to 350 F. Then spray 8x8-inch pan with nonstick cooking spray.
Crust: Add the flour, sugar, and salt into mixing bowl or food processor and pulse until combined. Add butter and continue pulsing until the pieces of butter are very small and the mixture is crumbly. Set aside 3/4 cup of this mixture to a small bowl to use topping. Transfer the remainder of the mixture into the prepared pan and press into an even layer to form the crust. Bake for 12-15 minutes, or until golden and set. Remove the pan to a wire rack and allow to cool for at least 10 minutes.
Filling: Whisk together the eggs, sugar, sour cream, flour, salt, lemon zest, and almond extract in medium bowl until well combined. Use a spatula to gently fold in the blackberries. Spread the filling evenly over the crust. Top the filling with the reserved crust mixture.
Bake for 40-50 minutes, or until the bars are set. Transfer the pan to a wire rack and allow the bars to cool completely in the pan.