In the bowl of a standing mixer, combine the warm water, molasses, and active dry yeast. Stir until all the grains dissolve. Let sit until foamy, about 10 to 15 minutes.
In a separate mixing bowl, whisk together your flours, Dutch cocoa powder, salt, and caraway seed.
With your dough hook attachment, set your mixer to low and pour in your dry ingredients. Gradually add the melted butter and egg. Mix until the dough pulls away from the sides of the bowl.
Shape your dough into a round and transfer to a lightly greased container. Cover and let your dough rise until double in size, about 1 hour to 1 1/2 hours.
Shape your dough into a sandwich loaf and transfer to a lightly greased 9-inch by 5-inch bread pan. Cover and let rise until dough is above the lip of the pan, about 45 minutes to 1 hour.
Preheat your oven to 400 degrees Fahrenheit (204° Celsius).
Beat together the egg with 1 tablespoon of water to create an egg wash. Brush the egg wash mixture over the top of the bread. Sprinkle with caraway seeds.
Bake your bread for 20 minutes. Tent with aluminum foil, and then bake another 20 to 25 minutes until internal temperature reads between 195° and 200° Fahrenheit (90° and 93° Celsius). Bottom will sound hollow when thumped.
Turn out loaf onto a wire cooling rack. Let cool completely before slicing and serving.