Light Rye:
Combine water and yeast in a large bowl. Let stand until foamy, about 5 minutes. Whisk in molasses and salt until dissolved. Add both flours, caraway seeds, and oil, stirring until a ragged dough forms. (Dough should be soft and tacky but not sticky -- add more bread flour, 1 tablespoon at a time, if dough is too wet; or water, 1 tablespoon at a time, if too dry.) Transfer to a clean work surface. Knead until smooth and elastic and dough springs back when lightly pressed, about 5 minutes. Transfer to a bowl brushed with oil, turning dough to evenly coat. Cover with plastic wrap and let rise until doubled in volume, 45 minutes to 1 hour.
Dark Rye:
Repeat process for light rye, adding cocoa powder to yeast mixture along with flours.
Preheat oven to 450 degrees. Punch down doughs and transfer to a clean work surface. Roll out each to an approximately 10-by-15-inch rectangle. Place darker dough on top of lighter dough. Starting at one short end, roll up doughs into a log. Pinch ends and seam together to seal. Gently roll back and forth with palms, applying more pressure toward edges, to shape into an approximately 13-inch-long torpedo (an Italian-baguette shape). Transfer to a parchment-lined baking sheet, seam-side down. Loosely cover and let rise until doubled in volume, 45 minutes to 1 hour. Using the tip of a sharp knife, make three 1/2-inch-deep diagonal slashes evenly across top of dough. Whisk egg white with 1 teaspoon water in a small bowl. Brush dough with egg wash; sprinkle generously with caraway seeds.
Transfer dough on sheet to oven. Reduce temperature to 350 degrees and bake until puffed and golden brown, and a thermometer inserted in center registers 200 degrees, 40 to 45 minutes. Let cool completely on sheet on a wire rack before slicing and serving.