Place whole wheat bread flour, rye flour, cocoa powder, bread flour, wheat germ, caraway seeds, yeast, beer, coffee, vinegar, olive oil, honey, molasses, sea salt, and onion powder in a bread machine in the order suggested by the manufacturer. Set bread machine for kneading cycle.
Line a baking sheet with parchment paper.
Remove dough from bread machine and shape into a rustic loaf on the prepared baking sheet. Make slits on top of loaf in crisscross formation. Let dough rise for 1 hour.
Preheat oven to 395 degrees F (202 degrees C).
Whisk egg white and warm water together in a small bowl. Brush egg white mixture over top of loaf.
Bake in the preheated oven until bread is cooked through, 45 to 50 minutes. Cool bread on a wire rack for 1 hour before serving.