Special equipment: ten 12-inch square sheets of aluminum foil; a disposable pastry bag fitted with a large star tip
Preheat the oven to 400 degrees F. Spray a baking sheet with nonstick spray.
Fold a 12-inch square sheet of aluminum foil in half, turn and fold in half again; you should have a small square. Now, fold diagonally and once more again. You will now have a triangle. Wrap it around your index finger and mold into a cone shape. Repeat 9 more times to make 10 molds. (Note: these can be reused.) Lightly spray the foil molds with nonstick spray.
Lay out the puff pastry sheet on a work surface with one of the long sides facing you. Cut the pastry into 3/4-inch-wide strips from top to bottom to make 20 strips. Wrap 2 pastry strips around each mold, overlapping a little with each wrap. Transfer to the prepared baking sheet and bake until lightly browned around the edges, 16 to 18 minutes. Let cool.
Meanwhile, whisk together the cream cheese and butter in a bowl. Add the confectioners' sugar in batches with the salt. Gently fold in the blackberry preserves (so there is some veining). Transfer to a disposable pastry bag fitted with a large star tip and place in the fridge for at least 30 minutes to let the filling firm up.
Pipe the filling into each pastry from the wider end. Serve with a dusting of confectioners' sugar and some blackberries and mint.