How to Make It
In a food processor, pulse the flour with the salt. Add the vegetable shortening and pulse until the mixture resembles coarse meal. Add the ice water to the mixture all at once and pulse just until the pastry comes together. Scrape the pastry out onto a lightly floured work surface and pat the pastry into an 8-inch square. Wrap the pastry square in plastic and refrigerate until it is firm, at least 30 minutes or overnight.
In a small bowl, mix the 1 cup of sugar with the cornstarch. In a large bowl, gently toss the peaches with the blackberries. Add the sugar-and-cornstarch mixture and lemon juice to the mixed fruit and gently toss the fruit again. Spoon the fruit into a 3-quart shallow glass or ceramic baking dish and scatter the pieces of unsalted butter over the top of the fruit filling.
Position racks in the middle and lower third of the oven and preheat the oven to 425°. Line a large rimmed baking sheet with aluminum foil. On a lightly floured work surface, roll out the cobbler pastry until it is 2 inches larger than the baking dish on all sides and about 1/8 inch thick.
Drape the cobbler pastry over the baking dish and trim the overhang to 1 inch. Fold the overhang under itself and press it lightly onto the rim of the baking dish; crimp the pastry edge decoratively. Brush the pastry with the half-and-half and sprinkle it with 1 tablespoon of sugar. Using a paring knife, make 6 small slits in the pastry crust to allow steam to escape.
Slide the aluminum foil-covered baking sheet onto the lower oven rack and bake the peach and berry cobbler on the middle oven rack for 50 minutes, or until the pastry is crisp and golden brown and the fruit filling is bubbling. Transfer the cobbler to a wire rack and let it cool for at least 1 hour or for up to 4 hours.