First, make the tangzhong. In a small skillet, add the water, milk, and bread flour. Whisk to combine and remove any lumps.
Transfer to the stove and turn the heat on to low. Cook, whisking constantly, until the mixture thickens and the whisk leaves lines on the bottom of the pan, about 3 minutes.
Transfer to a small container and let cool to lukewarm.
Next, make the dough. In your mixing bowl or breadmaker pan, add the tangzhong, 115 grams of milk, the egg, sugar, and melted butter.
Add the bread flour, milk powder, yeast and salt.
Mix and knead, until a smooth, elastic dough forms, 15 to 18 minutes. If using a breadmaker, transfer the pan to your machine, and start the Dough Program and let the machine finish the knead cycle.
Transfer the dough to a lightly oiled surface.
Divide the dough into 2 equal-sized pieces.
Shape one piece of dough into a ball. Set aside.
In a small bowl, add the cocoa powder and remaining 15 ml (1 tablespoon) milk. Stir until thoroughly combined.
Work the cocoa paste into the second piece of dough, until evenly combined.
Shape the chocolate dough into a ball.
Place the dough balls in lightly oiled bowls and let rest in a warm place, covered, until doubled in size, 1 hour.
Transfer the white dough to a lightly oiled surface. Gently press down the dough to let out the air. Reshape the dough into a ball. Repeat with the chocolate dough. Cover and let rest, another 15 minutes.
Lightly grease a 9- by 5-inch loaf pan with butter.
After the dough has rested, roll the white dough into a 6- by 8-inch rectangle. The short edge should be facing you.
Repeat with the chocolate dough.
Stack the white dough on top of the chocolate dough.
Leaving about 2 inches of space from the top, cut 8 to 9 slits along the length of the dough.
Working with one strip at a time, twist the dough 3 or 4 times.
Stretch out the top part of the dough to the same width as the twisted parts.
Starting from the bottom, roll the dough tightly upward.
Place the roll in the loaf pan.
Cover and let rise, another 30 minutes.
Towards the end of the rest time, preheat the oven to 180 degrees C (fan 160 degrees C).
Sprinkle the top of the loaf with flour.
Transfer to the oven and bake, 20 minutes.
Remove the loaf from the pan immediately, and let cool on a wire rack.