For the crust and topping:
For the filling:
Preheat the oven to 350˚ F. Line a 9 x 9-inch baking pan with foil and grease lightly. In the bowl of a food processor or electric mixer, combine the flour, sugar, salt and lemon zest. Pulse briefly to blend. Cut the butter into small cubes, then add to the bowl with the dry ingredients. Process in short pulses to cut the butter into the dry ingredients until only small pieces of butter remain and the mixture is crumbly.
Reserve ¾ cup of the mixture for topping the bars. Add the rest of the mixture to the prepared pan and press to form an even layer of crust on the bottom of the pan. Bake 12-15 minutes, until light golden. Let cool 10-15 minutes before proceeding.
In a medium bowl, make the filling mixture. Combine the eggs, sugar, sour cream, flour, salt, lemon juice and vanilla. Whisk until smooth. Gently stir in the blackberries with a spatula. Spread the filling mixture over the pre-baked crust in the baking pan. Crumble the reserved topping mixture over the filling evenly.
Bake until the top is beginning to brown and the bars are just set, about 45 minutes. Let cool completely on a wire rack. Chill to firm up before slicing and serving.