Preheat your oven to 350°F. Line an 8 x 8-inch baking pan with foil, leaving an overhang on two sides for easy removal. Lightly coat with nonstick spray.
In the bowl of a food processor, combine the sugar, flour, and salt. Pulse briefly to mix.
Add the cold butter and pulse until the mixture resembles coarse crumbs with pea-sized butter pieces.
Remove about 3/4 cup of the crumb mixture and set aside for the topping.
Press the remaining crumbs firmly into the prepared pan to form an even crust.
Bake for 12 to 15 minutes, until the edges are just beginning to turn golden. Remove and let cool completely.
In a medium bowl, whisk together the eggs and sugar until smooth. Add the sour cream, flour, and salt, mixing until fully combined.
Spread the blackberries evenly over the cooled crust.
Carefully spoon the filling over the berries, spreading gently to cover.
Sprinkle the reserved crumb mixture evenly over the top.
Bake for 45 to 55 minutes, until the top is lightly golden and the filling is set.
Cool completely on a wire rack before lifting out and slicing. Refrigerate if desired for cleaner cuts.