Preheat oven to 375°. Line 2 rimmed baking sheets with parchment paper.
In a large bowl, whisk together bread flour, cake flour, sugar, baking powder, and salt. Using a pastry blender or 2 forks, cut in cold butter until it resembles coarse crumbs. Add apricots and pistachios, stirring well.
In a small bowl, whisk together buttermilk and 1 egg. Add buttermilk mixture to flour mixture, stirring until mixture is evenly moist. (If dough seems dry, add more buttermilk, 1 tablespoon at a time.) Working gently, bring mixture together with hands until a dough forms.
Turn out dough onto a lightly floured surface, and gently knead 5 to 7 times. Using a rolling pin, roll out dough to a ¾-inch thickness. Using a 2¼-inch round cutter, cut 15 scones from dough, rerolling scraps as necessary.
In a small bowl, whisk together 1 teaspoon water and remaining 1 egg. Brush top of scones with egg wash.
Bake until edges of scones are golden brown and a wooden pick inserted in centers comes out clean, 15 to 20 minutes. Serve warm.
Recipe by TeaTime Magazine at https://teatimemagazine.com/apricot-pistachio-scones/