01 - Stir the active dry yeast and 1 tablespoon of sugar into the lukewarm milk. Let the mixture stand for 10 minutes until it becomes foamy and bubbly on the surface.
02 - In a large mixing bowl, whisk together the all-purpose flour, 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 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 and knead by hand or with a stand mixer fitted with a dough hook for 8 to 10 minutes, until the dough is soft, smooth, and elastic. Fold in the chopped dark chocolate during the final 2 minutes of kneading.
05 - Transfer the dough to a clean, lightly oiled bowl. Cover tightly with plastic wrap and let it rise in a warm, draft-free spot for 1 to 2 hours, or until doubled in volume.
06 - Gently punch down the risen dough and divide it into 8 equal portions. Shape each piece into a smooth oval bun and arrange them on a baking tray lined with parchment paper, leaving space between each for expansion.
07 - Loosely cover the shaped buns with a clean kitchen towel or oiled plastic wrap. Allow them to rise for 40 minutes until puffy and nearly doubled.
08 - While the buns are rising, preheat the oven to 355°F. Whisk the egg yolk with 2 tablespoons of milk and gently brush the mixture over the tops of each bun 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 them cool completely.
10 - In a chilled mixing bowl, whip the heavy cream with powdered sugar and vanilla extract using an electric mixer until firm, stable peaks form. Gently fold in the melted and cooled dark chocolate with a spatula until evenly incorporated.
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.