In a large bowl weigh or measure the flour, salt, baking powder, and baking soda together. I run a whisk through the dry ingredients to blend. Set the bowl aside. Zest and juice your lemon into separate bowls and set them aside. Finally, weigh or measure the sugar.
Using a hand or stand mixer, blend the sugar and butter until light and fluffy, about 2 to 3 minutes on a medium mixer speed. Next, add one egg at a time and mix through before adding the milk and vanilla extract. Scrape down the sides and turn the mixer to a slow speed. Slowly add the flour mixture and incorporate. Blend but don't over mix; you can combine any flour pieces at the bottom of the mixer bowl by hand. Place the dough onto a lightly floured pastry sheet and divide it into 2 rectangular-shaped blocks.
What you want to do is form a log shape after you roll the cookie dough. But cookie dough can stick when you are trying to roll it. So, I use a flat sheet of parchment paper that I lightly flour and use a rolling pin to form a rectangular shape. Using the parchment paper lets you get under the rolled-out cookie dough. If you do this on a counter and it sticks, it will be tough to get it to roll.
After creating the rectangular shape, spread a layer of the blackberry mixture on the dough. I leave 2 to 3 inches around the edges with no blackberry filling. This way, it doesn't squeeze out all over the place when you get to the end of rolling the dough into a log shape. Gentle start the roll and continue until it is in a log shape.
Wrap the log with plastic wrap. I use a paper towel cardboard insert cut length-wise to cradle the log and helps keep its shape. Do the same thing with the other block of cookie dough. Put both wrapped logs into the refrigerator for at least 1 to 2 hours, or I like to keep mine in the fridge overnight; it makes it easier to slice.
Heat your oven to 350°F (175°C or 180°C), and line 2 cookie sheet pans with parchment paper. Take a roll from the fridge and unwrap from the plastic wrap. Using a sharp knife, I slice off the ends if they do not have any filling and slice the rest of the roll in ¼ - ⅜ inch-thick slices. I put 12 slices onto a prepared sheet pan. Bake for 10-12 minutes until just a little golden brown.
After I pull the cookies from the oven, I put parchment paper or wax paper onto my wire rack. If I do not, the blackberry filling sticks to the wire rack, and half the cookie might stay on the wire rack as you take the cookies off.