Combine warm water, whole-wheat flour, and yeast in a small bowl. Let stand until the yeast softens and begins to froth and bubble, about 10 minutes.
Mix rye flour, molasses, cocoa powder, vegetable oil, coffee granules, caraway seeds, and salt in a large bowl. Add yeast mixture and all-purpose flour. Turn dough onto a floured surface; knead until smooth and elastic, about 10 minutes. Grease a large bowl.
Transfer dough to greased bowl; cover with warm damp towel or plastic wrap. Let rise in a warm area until doubled in size, about 1 hour.
Preheat an oven to 450 degrees F (230 degrees C). Grease a baking sheet.
Bring water to a boil in a large pot. Divide dough into 13 pieces; shape into balls. Press a hole into the center of each dough ball; pull dough to form a 1-inch hole in the center, keeping dough about 1/2-inch thick. Drop dough circles into boiling water, 3 or 4 at a time. Boil each side for 45 seconds. Remove with a slotted spoon and drain for about 1 minute. Arrange boiled bagels on prepared baking sheet.
Bake bagels in the preheated oven until just starting to brown on the bottom, 8 to 10 minutes.