Make the pastry as directed, adding the crystallized ginger, if desired, when you scatter the cheese cubes over the mixture and then pulsing just until the ingredients come together in a ball.
Divide the dough in half, shape each half into a 5-inch disk about ¾ inch thick (12 ½ ounces/355 grams), wrap in plastic wrap, and refrigerate until firm, about 4 hours.
Center a rack in the oven and preheat the oven to 375 degrees F. Place six 1-cup ramekins or custard cups each about 4 inches in diameter on a large rimmed baking sheet.
To prepare the fruit:
In a large bowl, gently toss together the berries, sugar, cornstarch, tapioca, cinnamon, nutmeg, and salt. Divide the fruit mixture evenly among the ramekins. Spoon 1 teaspoon of the cream over the fruit in each ramekin, and then top with a small pat of butter.
To top the potpies:
On a lightly floured work surface, roll out 1 disk of the dough about 3/16 inch thick. Using a 4½-inch round cookie or biscuit cutter (or other template), cut out circles. (You need circles that are just a bit larger than the diameter of your ramekins, so adjust the size as needed if your ramekins are a different diameter.) Set a pastry circle on top of each fruit-filled ramekin and, using your fingertips, gently press the pastry down into the ramekin around the edges. (The pastry doesn’t need to be sealed to the edges. As the potpies bake, the pastry will appear to “melt” and “hug” the fruit.) Roll out the second dough disk and cut out circles to cover the remaining ramekins.
With a pastry brush, apply a light coating of water to the pastry on each ramekin, and then sprinkle some sugar over the top. Using a small paring knife, make a couple of slits in the center of each pastry to allow steam to escape.
Bake the potpies until the pastry is golden and the fruit is bubbly, 30 to 35 minutes. Transfer to a wire rack to cool Serve warm or at room temperature (the fruit filling will thicken as it cools).