In a food processor or bowl, combine 2 cups flour, 2/3 cup granulated sugar, cocoa, baking powder, baking soda, and salt; whirl or mix until blended.
Cut butter into 1/2-inch chunks and add to flour mixture. Whirl, cut in with a pastry blender, or rub in with your fingers until mixture forms fine crumbs; pour into a bowl if using processor.
In a small bowl, whisk egg yolks with buttermilk to blend; add to flour mixture and stir just until evenly moistened.
Turn dough out onto a floured board and, with lightly floured hands, knead just until it comes together. Pat out to about 1 1/4 inches thick. With a 3-inch round cutter, cut out shortcakes; gather dough scraps and pat out again as necessary to make all six shortcakes. Set 2 inches apart on a 14- by 17-inch baking sheet.
Bake on the middle rack in a 375° regular or 350° convection oven until tops look dry and feel firm when pressed, about 25 minutes. Transfer shortcakes to a rack and let cool completely.
Meanwhile, rinse raspberries. In a blender or food processor, whirl half the berries with the remaining 2 tablespoons granulated sugar until smooth. Press through a fine strainer into a bowl; discard residue.
To assemble shortcakes, slice each in half horizontally; set bottoms on plates. Spoon vanilla crème fraîche over bottoms, top with remaining berries, and drizzle with raspberry sauce. Place shortcake tops over berries and sprinkle with powdered sugar.