• For the crust
1 cup (142 grams) all-purpose flour, plus more for the work surface
3/4 cup (103 grams) barley flour (see headnote)
1/2 cup (74 grams) fine stone-ground yellow cornmeal
1 teaspoon sugar, plus more for optional sprinkling
1/2 teaspoon salt
10 tablespoons (1 stick plus 2 tablespoons) cold unsalted butter, cut into 1/2-inch cubes
1/3 cup (75 grams) cold fresh grapefruit juice
1 large egg, lightly beaten, for egg wash (optional)
• For the filling
3/4 cup (156 grams) sugar
5 tablespoons cornstarch, sifted
1/2 teaspoon ground coriander
1/4 teaspoon salt
1 3/4 pounds (about 5 1/4 cups) fresh blueberries
1 1/2 pounds very ripe nectarines (about 5), pitted and cut into 1/2-inch cubes (3 1/2 cups)
3 tablespoons fresh grapefruit juice
Water
• For the crust: Combine both flours, the cornmeal, sugar and salt in a food processor and pulse until well mixed. Add the butter and pulse until the mixture forms coarse crumbs, with a few almond-size pieces remaining. Sprinkle the grapefruit juice over the mixture, and pulse until the dry ingredients are evenly moistened and large clumps just start to form. When you squeeze some of the fine crumbs between your fingers, they should hold together.
Turn out the dough and divide it into 2 portions, one slightly larger than the other. Shape the dough into two 1-inch-thick disks. Wrap each in plastic wrap and refrigerate until firm, at least 2 hours.
Lightly flour a large sheet of parchment paper. Unwrap the larger disk of dough, place it in the center of the paper and cover it with its plastic wrap. Roll into a 12-inch round, occasionally lifting and replacing the plastic wrap. Flip it over and peel off the parchment, then lift the dough with the plastic wrap and flip it into a 9-inch pie plate, gently pressing it into the bottom and up the sides. Discard the plastic. Refrigerate until ready to fill.
Unwrap the remaining disk of dough and repeat the rolling, using the same parchment and rolling the dough into an 11-inch round. If the dough has softened, slide it on the parchment onto a pan and refrigerate until firm. Use a fluted or straight-edged pizza/pastry cutter or a sharp knife to cut the remaining dough into 1/2-inch-wide strips. Slide onto a large flat plate or pan and refrigerate.