Activate the yeast in the warm milk and sugar. Let it sit for 5 minutes. After it has activated, add the remaining ingredients with the yeast mixture to your stand mixer or large bowl, except the cocoa and 1 tablespoon of rye flour. Knead with the dough hook attachment until you have a smooth dough and slightly sticky. I like to start on low speed for the first 30 seconds, then increase to a medium speed. Mix for 5-7 minutes until the dough is smooth.
Cover the dough with plastic wrap and let the dough rise at room temperature for about 1- 1 ½ hours until the dough has doubled.
Divide the dough in half. Mix the cocoa and tablespoon of rye flour and knead them into half of the dough. I added in a tablespoon of water to help me knead it in more smoothly. This is going to be messy, so be ready. Once you have the dough colored, it is time to form the loaf.
I like to divide the light rye dough and the dark rye dough in half so you have 4 pieces. On a lightly floured surface roll each one to a 6-inch by 10-inch rectangle with a rolling pin.
Alternate the layers on top of each other, then roll up to form the loaf. The dark dough and the light dough will form a beautiful swirl in the bread.
Place it into your prepared pan, with the seam side down, cover and let it rise for the second time until it has doubled again.
Preheat the oven, brush the top of the loaf with egg wash, score if you are doing it, then bake.
The oven is preheated to 400 degrees. It will bake at this high temp for 15 minutes, then reduce the oven temperature to 350 degrees. Bake for an additional 20-30 minutes. Be sure to check the internal temperature- you want it to be at 195 degrees.