In a small bowl, stir together the milk, sugar, and yeast. Let sit for 10 minutes until the yeast is dissolved and bubbly.
Transfer the mixture to the bowl of a stand mixer fitted with a dough hook. Add the egg, sugar, flour, and salt. Knead on low speed until a soft dough begins to form. Add the butter, one cube at a time, kneading until each piece is fully incorporated before adding the next. Increase the mixer speed to medium and knead for 10 minutes, until the dough is smooth, elastic, and uniform. Transfer to a lightly oiled bowl, grease the top of the dough, cover with plastic wrap, and let rise for 40 minutes at room temperature. Repeat the same process with the cocoa dough.
Once both doughs have risen, gently press them down to deflate. Transfer to a lightly floured work surface. Divide each dough into 6 equal pieces, shape into balls, and cover with plastic wrap. Let rest for 10 minutes.
Roll each piece into a thin rectangle. Roll each cocoa dough portion into a long cylinder. Place each cylinder on a white rectangle and roll up to form a log, completely encasing the cocoa dough.
Grease a loaf pan well. Arrange the logs inside and cover loosely with plastic wrap. Let rise for 30 minutes.
Preheat the oven to 340°F (170°C).
Bake the loaf for 25 to 30 minutes, until puffed and golden brown on top. Let cool in the pan for 10 minutes, then remove and allow to cool completely before slicing and serving.