Line a baking sheet with parchment paper.
Using a bench scraper, cut shortening and cold unsalted butter into cubes, and freeze until ready to use.
In a small bowl, stir together 2 tablespoons (30 grams) warm water and yeast until yeast is dissolved.
In a medium bowl, whisk together flours, sugar, salt, baking powder, and baking soda. Place three-fourths of flour mixture in the work bowl of a food processor; add cold shortening and cold butter, and pulse until mixture is crumbly with some pea-size pieces of butter remaining. Return mixture to large bowl, and stir to combine with remaining flour mixture. (Alternatively, cut cold shortening and cold butter into flour mixture using a pastry blender.) Add yeast mixture and buttermilk, stirring just until dry ingredients are moistened. Cover and refrigerate for 1 hour.
Turn out dough onto a lightly floured surface, and knead 4 or 5 times. Pat dough to ¾-inch thickness. Using a 2½-inch round cutter, cut dough, re-patting scraps only once. Place on prepared pan. Cover and let rise in a warm, draft-free place (75°F/24°C) until puffed, about 1 hour.
Preheat oven to 375°F (190°C).
Brush biscuits with melted, salted butter, and bake until golden brown, 12 to 15 minutes. Let cool on pan for 5 minutes. Serve warm.