01 - In a small bowl, stir the active dry yeast and 1 tbsp of granulated sugar into the lukewarm 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, 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 activated yeast mixture. Stir with a wooden spoon until a shaggy dough begins to come together.
04 - Turn the dough 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. During the final 2 minutes of kneading, incorporate the chopped dark chocolate.
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 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 clean kitchen towel and let them rise for 40 minutes until puffed and nearly doubled.
08 - Preheat the oven to 355°F (180°C). In a small dish, whisk together the egg yolk and 2 tbsp of milk. Brush the mixture evenly over the tops of each bun for a glossy finish.
09 - Bake on the center rack for 15 to 18 minutes, until the buns feel slightly firm to the touch and are 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 peaks hold their shape. 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.