Add the warm water to the bowl of a food processor (or a large mixing bowl). Add the rye flour, bread flour, whole wheat flour, unsweetened cocoa powder, instant dry yeast, brown sugar, salt, and vegetable oil.
Mix the dough (food processor method): Pulse and then run the food processor just until a very soft, sticky dough forms and pulls away from the sides slightly. This takes about 5 minutes.
Optional hand-mixing method: Stir everything together with a sturdy spoon until no dry flour remains. The dough will be loose, sticky, and more like a thick paste than a kneadable dough.
Cover tightly and let rise at room temperature for 1 hour 30 minutes, until visibly puffy and expanded. It will not double fully.
Shape the loaf (two options)
Log method: Generously dust a work surface with rye flour. Turn out the dough (it will be very soft and sticky). Lightly dust the top and gently roll into a rough log shape. Transfer to a parchment-lined baking sheet.
Pan method (easiest): Simply scrape the dough into a lined or well-oiled loaf pan and smooth the top with wet or oiled hands.
Cover loosely and let rise for 40 minutes.
Preheat the oven to 425°F (220°C). Bake for 35–40 minutes, until the loaf is firm, deeply colored, and sounds hollow when tapped. Internal temperature should be about 200°F (93°C).
Remove from the oven and cool completely on a rack before slicing. This bread sets as it cools and slices best once fully cooled.
Notes
Wrap tightly and store at room temperature for up to 3 days or freeze for up to 3 months. Thaw at room temperature before using.