Add bread flour, caster sugar, salt, active dry yeast, beaten egg, and milk to a large mixing bowl. Knead the ingredients with a stand mixer fitted with a dough hook until a dough forms. Add the softened butter and continue to knead for 10 to 15 minutes, until the dough is smooth and elastic. (You may also knead the dough by hand.)
Cover the dough with plastic wrap and let it rise in a warm area for 40 minutes, or until doubled in size. Meanwhile, prepare the chocolate cake and preheat the oven to 302°F (150°C).
Melt the butter and chocolate bar in a small pot over low heat. Transfer the mixture to a large bowl and let it cool slightly. Next, whisk in the milk, egg yolks, and sifted cake flour. Mix until no dry flour remains, but be careful not to overmix. Set the batter aside.
Add the egg whites to a separate mixing bowl and beat with an electric hand mixer until foamy. Continue beating while adding the caster sugar in 3 batches, and keep beating until stiff peaks form.
Fold 1/3 of the whisked egg whites into the batter and gently mix to combine. Then, fold in the remaining egg whites and mix gently. Pour the batter into a 10" x 14" (25 x 35 cm) baking tin lined with parchment paper. Bake for 20 minutes. Once the cake is baked, remove it from the oven and let it cool. Unmold the cake and remove the parchment paper. Trim the edges and set aside.
Transfer the bread dough to a floured work surface. Roll out the dough into a rectangle slightly larger than the chocolate cake. Place the chocolate cake on top of the dough and roll it up tightly into a log, pinching the edges to seal. Transfer the log to a greased loaf tin. Cover the tin with plastic wrap and let it rise for 45 minutes, or until doubled in size.
Preheat the oven to 374°F (190°C). Brush the loaf with beaten egg and bake for 25 minutes, or until golden brown. Remove from the oven and let cool. Unmold and enjoy.