01 - In a small bowl, stir the active dry yeast and 1 tablespoon of granulated sugar into the lukewarm whole milk. Let the mixture stand for 10 minutes until it becomes foamy and bubbly, indicating the yeast is active.
02 - In a large mixing bowl, whisk together the all-purpose flour, unsweetened cocoa powder, remaining granulated sugar, and salt until evenly distributed.
03 - Create a well in the center of the dry mixture. Add the egg, vanilla extract, softened unsalted butter, and the activated yeast mixture. Stir with a wooden spoon until a shaggy dough begins to come together.
04 - Turn the dough out onto a lightly floured surface. Knead by hand or with a stand mixer fitted with a dough hook for 8 to 10 minutes, until the dough becomes soft, smooth, and elastic. During the final minute of kneading, fold in the chopped dark chocolate until evenly distributed throughout.
05 - Transfer the dough to a clean, lightly oiled bowl. Cover with a damp towel or plastic wrap and let rise in a warm, draft-free spot for 1 to 2 hours, or until the dough has doubled in size.
06 - Punch down the risen dough gently. Divide it into 8 equal portions. Shape each piece into an oval bun and arrange them on a baking tray lined with parchment paper, spacing them about 2 inches apart.
07 - Cover the shaped buns loosely with a damp towel or plastic wrap. Allow them to rise for 40 minutes until puffed and nearly doubled.
08 - Preheat the oven to 355°F. Whisk together the egg yolk with 2 tablespoons of milk to make an egg wash. Gently brush the tops of the risen buns with the egg wash for a glossy finish.
09 - Bake on the center rack for 15 to 18 minutes, until the buns are slightly firm to the touch and cooked through. Transfer to a wire rack and let cool completely before filling.
10 - In a chilled mixing bowl, whip the heavy cream with powdered sugar and vanilla extract using an electric mixer until firm peaks hold their shape. Gently fold in the melted and cooled dark chocolate with a spatula until uniformly combined, being careful not to deflate the cream.
11 - Using a serrated knife, slice each cooled bun lengthwise, leaving one side attached as a hinge. Generously pipe or spoon the chocolate whipped cream into each bun. Dust with additional powdered sugar if desired and serve immediately.