For the dough:
For the filling:
Preheat the oven to 425
In a bowl, using a fork, stir together the flour, granulated sugar, baking powder and salt. Add the butter and toss it well to coat with the flour mixture. Using a pastry blender or 2 knives, cut in the butter just until the mixture forms large, coarse crumbs the size of small peas. In a small bowl, whisk together the egg and the 1/3 cup (3 fl. oz./80 ml) cream until blended. Pour the egg mixture over the flour mixture and mix with a rubber spatula just until moistened.
Add additional cream, 1 tablespoon at a time, as needed to form a soft dough that is wet enough to be dropped from a spoon.
Using a large spoon, drop the dough onto the prepared baking sheet in mounds about 3 inches (7.5 cm.) wide and about 3/4 inch (2 cm.) high, spacing them 1 inch (2.5 cm.) apart. You should have about 8 shortcakes. Brush the tops of the shortcakes with 1-2 tablespoons cream and sprinkle with the turbinado sugar. Bake until the shortcakes are firm to the touch and golden-brown, 12-15 minutes.
While the shortcakes are baking, prepare the filling. In a bowl, using a fork, crush 1 cup (4 oz./125 g) of the berries. Add the remaining berries and the granulated sugar, mix well, and set aside. Transfer the shortcakes from the baking sheet to a wire rack and let cool for 15 minutes.
To serve, split the warm shortcakes horizontally and place the bottom half of each, cut side up, on a plate. Spoon the berries on top, dividing them evenly. Top each with some whipped cream. Cover with the shortcake tops and serve right away. Serves 8.