Heat the oven to 425°F (218°C).
In a large bowl, whisk the flour with the granulated sugar, baking powder, and salt.
In another bowl, toss the blackberries with the lemon juice and ¼ cup of the flour mixture. Set aside.
Using your fingers, rub the butter into the remaining flour mixture until it forms pea-size crumbles. Make a well in the center of the flour and pour the cream into the well. Stir until a dough begins to form, then stir in the floured blackberries, mint, and lemon zest.
Scrape the dough onto a lightly floured work surface and use a rolling pin to flatten into a ¾ -inch-thick disk. Fold the dough in half, and then flatten again. Repeat folding and rolling three more times, and then shape the dough into a disk, about ¾ -inch thick. Cut the circle into portions, and transfer each to a parchment paper-lined baking sheet.
Remove the scones from the freezer and brush with cream and sprinkle with turbinado sugar. Bake until puffed and golden brown, about 25 minutes. Transfer the scones to a rack and let cool for 10 minutes.
While the scones are baking, make the coffee according to the directions on the coffee maker.
Serve the scone with warm with coffee (with cream and sugar if desired).