Preheat oven to 400 F and line a pan with parchment paper.
Cut butter into half inch cubes. Set aside in a small bowl in the refrigerator while you complete the next steps.
In a large bowl, sift together the flour, baking powder, salt, and sugar.
Add the cold butter to the large mixing bowl of dry ingredients. Cut the butter into the flour mixture using a pastry blender until the mixture looks like coarse crumbs or a coarse meal.
Very gently, fold the fresh blackberries and lemon zest into the batter, taking care not to mash the fruit.
Make a well in the center of the dough, and pour the heavy cream into the middle.
Use a fork to very gently toss the dough, until a rough, shaggy dough forms. Again, don't mash those juicy blackberries!
Turn the scone dough out onto a floured surface and knead very gently, 2-3 times, until the dough comes together.
Shape the dough into a rectangle, roughly 12 x 3 x 1 1/4 inches. Cut the rectangle in half, then cut the pieces in half again, giving you 4 (3-inch) squares. Cut the squares in half on a diagonal, for a classic triangle shape. Alternatively, pat into a large, roughly 6-inch disc shape, and cut into 8 portions.
Place the scones on the prepared baking sheet. Brush the tops of the scones with heavy cream, and sprinkle with a bit of coarse sugar for some extra crunch.
Bake 15 to 20 minutes until golden brown. Let cool 5 minutes in the pan, then transfer to a wire rack to cool. Serve warm scones with some salted butter.