- Mix crushed and sliced berries with sugar and balsamic vinegar. Cover and refrigerate.
- With rack in lower middle, preheat oven to 425 degrees. Whisk together flour, salt, baking powder, and sugar.
- Using large holes of grater, grate cold butter into dry ingredients. Toss butter with dry ingredients to coat. Add lard. Using pastry cutter, finish cutting butter and lard into flour.
- Mix beaten egg with buttermilk; pour into flour mixture. Toss with fork until large clumps form. Turn mixture onto floured work surface and lightly knead until it comes together.
- On the lightly floured surface, pat dough into a ¾-inch-thick circle. Flour a 2½-inch biscuit cutter; cut 6 shortcakes. Place 1 inch apart on baking sheet; brush dough tops with egg white and sprinkle with granulated sugar. Bake until golden brown, 8−10 minutes.
- With mixer, beat cream, sugar, and vanilla on low until it thickens and is not splashing. Gradually increase speed to high, beating until cream is smooth, thick, and holds a peak.
- Split each cake in half; spoon berries and whipped cream over each cake bottom. Cover with cake top and serve immediately.