01 - Stir the yeast and 1 tablespoon of sugar into lukewarm milk in a small bowl. Let stand for 10 minutes until the mixture becomes foamy and bubbly.
02 - In a large mixing bowl, whisk together the all-purpose flour, cocoa powder, remaining 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 - 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 with a damp towel or plastic wrap and let rise in a warm spot for 1 to 2 hours, until doubled in volume.
06 - Gently punch down the dough and divide into 8 equal portions. Shape each piece into an oval bun and arrange on a parchment-lined baking sheet, spacing them about 2 inches apart.
07 - Cover the shaped buns loosely and let proof for 40 minutes until puffed and nearly doubled in size.
08 - Preheat the oven to 355°F. Whisk together the egg yolk and milk, then brush the mixture evenly over each bun for a glossy finish.
09 - Bake for 15 to 18 minutes, until the buns are slightly firm to the touch and cooked through. Transfer to a wire rack and cool completely.
10 - Whip the heavy cream with powdered sugar and vanilla extract to stiff peaks. Gently fold in the melted and cooled dark chocolate until uniformly combined.
11 - 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 powdered sugar if desired and serve immediately.