Dice the unsalted butter into small pieces then place it in the freezer to keep it chilled. In a bowl, mix together the greek yogurt, egg, vanilla extract, and lemon zest. Set it aside in the fridge to keep it chilled.
In a separate large bowl, add in the flour, granulated sugar, baking powder, and kosher salt. Whisk the ingredients together until evenly combined. Add in the cold diced butter. Use your fingertips to rub the pieces of butter into the dry mixture until you get a mixture that resembles wet sand with pea sized chunks of butter. Add the yogurt mixture into the dry mixture. Mix it together with a fork until the dough turns into scraggly ball of dough.
Dump the dough onto a floured surface. Gently press it into a 9 x 8 inch rectangle about a ½ inch thick. Distribute half of the sliced blackberries onto one half of the dough. Cut the dough in half then layer it on top of the half with blackberries. Gently press down to form it into 9 ½ x 7 ½ inch rectangle.
Scatter remaining blueberries on half of the dough. Cut the dough in half and layer it on top of the blackberries. Gently press down only to adhere the two layers. Wrap the dough in plastic wrap and freeze for 1 hour.
Preheat the oven to 350℉. Cut the dough into 6 evenly sized pieces. Place them onto a baking sheet lined with parchment paper, spacing them 2 inches apart. Brush the tops with heavy cream or whole milk. Then sprinkle raw sugar on top. Bake them in the oven for 30-33 minutes until golden brown on the outside. Transfer them to a wire rack to cool.