Combine the bread flour, sugar, salt, and instant yeast. Add the lukewarm whole milk and lightly beaten egg, then mix until a rough dough forms.

Knead the dough for several minutes, then add the softened butter gradually. Continue kneading until the dough is smooth, elastic, and only slightly tacky.

Shape the dough into a ball, cover it, and let it rise in a warm place for 60–90 minutes, or until doubled in size.

Deflate the risen dough and divide it by weight into three portions: about one-half plain, one-quarter for the light-cocoa dough, and one-quarter for the dark-cocoa dough.

Knead 10 g cocoa powder into the light portion and 20 g cocoa powder into the dark portion. Add milk a teaspoon at a time if either cocoa dough becomes dry or stiff.

Divide the brown doughs into several uneven pieces and roll them into irregular ropes. Loosely wrap the dark ropes with light-brown dough, then wrap some sections with plain dough.

Cut the combined ropes into shorter pieces and arrange them loosely in a greased 8 1/2 x 4 1/2-inch or 9 x 5-inch loaf pan. Leave space between pieces so the dough can expand.

Cover the shaped loaf and let it rise for 30–60 minutes, until visibly puffy. If desired, brush the surface with the egg wash.

Bake at 180°C/350°F for 35–40 minutes, until deeply golden and the center reaches approximately 93°C/200°F.

Cool the loaf in the pan for 10–15 minutes, then transfer it to a rack. Cool completely before slicing so the crumb sets cleanly.