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Step 1
For light dough: In the bowl of a stand mixer, whisk together 2⅓ cups (292 grams) all-purpose flour, rye flour, salt, yeast, and caraway seeds by hand until well combined. Add 1 cup (240 grams) warm water, oil, and molasses; using the paddle attachment, beat at low speed until combined, about 30 seconds, stopping to scrape sides of bowl.
Step 2
Switch to the dough hook attachment. Beat at low speed until dough is soft, tacky, and elastic and mostly cleans sides of bowl, 8 to 12 minutes, stopping to scrape sides of bowl and dough hook; add up to remaining ⅓ cup (42 grams) all-purpose flour, 1 tablespoon (8 grams) at a time, if needed. (Dough may still stick to bottom of bowl but should pass the windowpane test; see Note.) Transfer dough to a clean surface. Cover with a lightly greased sheet of plastic wrap.
Step 3
For dark dough: Clean bowl of stand mixer and attachments. In the bowl of a stand mixer, whisk together 2¼ cups (281 grams) all-purpose flour, rye flour, cocoa, salt, yeast, and caraway seeds by hand until well combined. Add 1 cup (240 grams) warm water, oil, and molasses; using the paddle attachment, beat at low speed until combined, about 30 seconds, stopping to scrape sides of bowl.
Step 4
Switch to the dough hook attachment. Beat at low speed until dough is soft, tacky, and elastic and mostly cleans sides of bowl, 8 to 12 minutes, stopping to scrape sides of bowl and dough hook; add up to remaining ¼ cup (31 grams) all-purpose flour, 1 tablespoon (8 grams) at a time, if needed. (Dough may still stick to bottom of bowl but should pass the windowpane test; see Note.)
Step 5
On a clean surface, shape light and dark doughs into balls. 6. Lightly oil 2 large bowls. Place doughs in bowls, turning to grease tops. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 40 minutes to 1 hour.
Step 6
Punch down doughs; cover and let stand for 10 minutes. Turn out doughs onto a clean surface. Divide each dough into 4 portions (about 178 grams each). For one loaf, roll 2 light dough portions and 2 dark dough portions into 9x6-inch rectangles. Layer rectangles on top of one another, starting with light and ending with dark. Reroll or pat stacked dough into a 9x6-inch rectangle, making sure to get out any air bubbles between layers. Starting at one long side, roll up dough, jelly roll style. Repeat procedure with remaining dough.
Step 7
Spray 2 (9x5-inch) loaf pans with cooking spray. Place dough logs, seam side down, in prepared pans. (Alternatively, pinch ends to seal, and tuck under to secure; roll dough into about a 9½ -inch log [about 3 inches wide]. Repeat procedure with remaining dough, and place dough logs 3 inches apart on a parchment paper-lined baking sheet.) Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 40 minutes to 1 hour.
Step 8
Preheat oven to 375°F (190°C).
Step 9
For topping: In a small bowl, whisk together egg and
Step 10
tablespoon (15 grams) water. Brush loaves with egg wash. Sprinkle with caraway seeds. Using a small sharp serrated knife, make 4 diagonal slashes that are ½ to ⅜ inch deep and 4½ to 5 inches long across top of loaves.
Step 11
Bake for 15 minutes; rotate pans, and bake until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), 10 to 12 minutes more. Remove from pans, and let cool completely on a wire rack. Store in an airtight container for up to 3 days.