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 attached to a dough hook until a dough forms. Add softened butter and continue to knead for 10 to 15 minutes until smooth and more elastic. (You may also knead the dough by hand).
Cover the dough with plastic film and let it rise in a warm area for 40 minutes until doubled in size.
Meanwhile, let's prepare the chocolate cake. Preheat oven to 302°F (or 150°C).
Melt the butter and chocolate bar in a small pot over low heat, then transfer the mixture to a large bowl and let it cool down for a little bit. Next, whisk in milk, egg yolks, and sifted cake flour. Mix until no powder left. Do Not over mix the batter. Set the batter aside.
Add the egg whites to a separate mixing bowl, and beat it with an electric hand mixer until foamy. Keep beating the egg white while adding the caster sugar in 3 batches, and continue to beat until stiff peak forms.
Fold in 1/3 of the whisked egg white into the batter, and gently mix to combine well. Then, fold the mixture into the remaining whisked egg white 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 allow it to cool. Unmold it and remove the parchment paper. Trim the edges and set aside.
Transfer the bread dough to a floured working 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. Pinch the edges to seal.
Transfer the whole piece to a loaf tin greased with butter. Cover the tin with plastic film and let it rise for 45 minutes until doubled in size.
Preheat the oven to 374°F (or 190°C). Brush with beaten egg and bake for 25 minutes until golden brown. Remove from the oven and cool down. Unmold and enjoy.