01 - Combine the yeast and 1 tablespoon of sugar in lukewarm milk. Stir gently and let the mixture rest for 10 minutes until it becomes frothy and activated.
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 comes together.
04 - 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. Incorporate 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 it rise in a warm spot for 1 to 2 hours until doubled in volume.
06 - Punch down the risen dough and divide it into 8 equal portions. Shape each piece into an oval bun and arrange them on a parchment-lined baking tray, leaving space between each for expansion.
07 - Cover the shaped buns loosely and allow them to proof for 40 minutes until puffy and nearly doubled in size.
08 - Preheat the oven to 355°F (180°C). Whisk together the egg yolk and 2 tablespoons of milk, then 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 are slightly firm to the touch and cooked through. Transfer to a wire rack and let them cool completely.
10 - Using an electric mixer, whip the heavy cream with powdered sugar and vanilla extract to firm, stable peaks. Gently fold in the melted and cooled dark chocolate until evenly incorporated, being careful not to deflate the cream.
11 - Slice each cooled bun lengthwise, keeping one side attached as a hinge. Pipe or spoon a generous amount of chocolate whipped cream into each bun. Dust with powdered sugar if desired and serve immediately.