For light dough: In a large bowl, combine all-purpose flour, rye flour, butter, honey, salt, and yeast. Gradually add 1 cup water, beating until a soft dough forms. Turn out dough onto a lightly floured surface, and knead dough until smooth and elastic, about 10 minutes.
For dark dough: In a separate large bowl, combine all-purpose flour, rye flour, butter, cocoa, molasses, salt, and yeast. Gradually add 1 cup water, beating until a soft dough forms. Turn out dough onto a lightly floured surface, and knead dough until smooth and elastic, about 10 minutes. Shape each mass of dough into a ball. Spray 2 large bowls with cooking spray. Place dough in bowls, turning to grease tops. Cover and let stand in a warm, draft-free place (75°F) until doubled in size, about 1 hour.
Turn out dough onto a lightly floured surface, and deflate it to remove excess air. Divide each ball in half. Roll each dough quarter into a 9x6-inch rectangle. Layer rectangles on top of one another, alternating light and dark. Starting at one long side, roll dough into a log. Spray a 9x5-inch loaf pan with cooking spray. Place loaf seam side down in pan. Cover and let rise in a warm, draft-free place (75°F) until doubled in size, about 1 hour.
Preheat oven to 375°F.
For topping: In a small bowl, whisk together egg and 1 tablespoon water. Brush egg wash over loaf. Using a sharp knife or lame, make 4 deep slashes across top of loaf. Sprinkle with caraway seeds and flax seeds. Bake until golden brown and an instant-read thermometer inserted in center registers 190°F, 35 to 40 minutes. Let cool in pan for 20 minutes. Remove from pan, and let cool completely on a wire rack.
Recipe by Bake from Scratch at https://bakefromscratch.com/?p=384