Preheat oven to 325°F. Lightly grease a 9-inch springform or square baking pan, set aside.
In a large mixing bowl, whisk together the flour, salt, baking powder, baking soda and sugar. Make a well in the center.
In a medium mixing bowl whisk the eggs until blended. Add the sour cream, vanilla, lemon juice and lemon zest. Whisk until blended. Slowly add the melted butter whisking constantly until combined. Pour the sour cream mixture into the flour and sugar mixture. Stir with a spatula until the dry ingredients are moistened. The batter will be very thick.
Pour ⅔ of the batter into the prepared pan. Sprinkle 1 cup of blackberries over the batter. Dollop the remaining batter over the blackberries, and smooth with an offset spatula. Top with all remaining blackberries, pressing the berries slightly into the batter.
Allow the cake to rest for 10 to 15 minutes before baking. Sprinkle coarse sugar on top, mostly on the exposed batter avoiding the blackberries.
Bake at 325°F for 60 to 70 minutes or until a toothpick or knife inserted into the center comes out with no wet batter. Moist crumbs are okay.
Cool the cake for 20 minutes, then remove the sides of the springform pan. Slide the cake onto a serving platter or plate. Serve slightly warm or at room temperature. Dust with powdered sugar, or a dollop of whipped cream, if desired.
If using a square cake pan, serve straight from the pan.