Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Whisk the flour, granulated sugar, baking powder, and salt together in a large bowl. Add the butter and work it into the flour mixture using a pastry cutter or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces remaining.
Gently fold in the blackberries, breaking a few slightly to create streaks of color throughout the dough.
Whisk the heavy cream, egg, vanilla extract, and lemon zest together in a small bowl. Pour the mixture into the dry ingredients and stir until a shaggy dough forms.
Transfer the dough to a lightly floured surface and gently press it together into a 1-inch-thick circle. If the dough feels too sticky to handle, dust some additional flour on top.
Cut the dough into 8 wedges and transfer them to the prepared baking sheet, spacing them slightly apart.
Brush the tops lightly with heavy cream.
Bake for 18-20 minutes, until golden brown around the edges and cooked through. Cool the scones on the baking sheet for 10 minutes.
Meanwhile, whisk the confectioners’ sugar, lemon juice, and vanilla extract together in a small bowl until smooth. Add additional lemon juice as needed to reach a pourable consistency.
Drizzle the glaze over the slightly warm scones before serving.