Preheat oven to 350F. Line a 7 x 11-inch baking pan with parchment paper and set aside. (Alternately, you can use a 9x9-inch baking pan).
Add the flour, sugar and salt to a food processor. Pulse a few times to combine. With the processor running, add the butter cubes and then switch to pulse and pulse until the mixture is crumb-y, with just small pieces of butter visible. Remove 3/4 cup of the mixture and set aside. Pour the remaining mixture into your prepared pan and press down lightly and evenly.
Bake in preheated oven for 12-15 minutes, or until set. Remove from oven, leaving oven on. Allow to cool 10 minutes.
Meanwhile, prepare the filling by whisking together the eggs, sugar, sour cream, flour, salt and vanilla in a medium bowl. Once crust has cooled 10 minutes, pour filling overtop of the crust. Scatter the blackberries evenly overtop. Top with the reserved crumb mixture, scattering it here and there, but allowing some of the blackberries to peek out.
Bake in preheated oven until set and lightly golden. For fresh blackberries, this can be as little as 35-40 minutes. For frozen blackberries, this can be as much as 55-60 minutes. Also, if you are using a 9x9-inch pan, the squares will be slightly thinner, so may cook a little more quickly.
Remove from oven. You can enjoy "cobbler style" right from the oven or allow to cool completely then cut into squares. Store in the fridge once cooled, but tastes best at room temperature or warmed lightly. These also freeze well.