Dry Mix

• 1 cup rye flour
• 2 cups all-purpose flour
• ¼ cup sugar
• 1½ teaspoons kosher salt
• 6 ounces (1½ sticks) unsalted butter, frozen

Wet Mix

• 1 package plus 1 teaspoon active dry yeast
• ¾ cup whole milk, warmed to about 100°F
• 1 egg

Filling

• 3 tablespoons unsalted butter, softened to room temperature
• ¼ cup maple sugar
• 2 tablespoons dark brown sugar

1. Sift the dry ingredients into a large bowl, pouring back into the bowl any bits of grain or other ingredients that may remain in the sifter. Using the large holes on a box grater, quickly grate the frozen butter into the dry mixture—this will ensure that the butter stays cold. With your hands, very briefly stir the strands of butter into the mix and then chill while you continue with the recipe.
2. Measure the yeast and warm milk into a small bowl. Stir and allow the yeast to bloom for about 5 minutes, or until the yeast begins to bubble. (If it doesn’t, it may be inactive; throw it out and start over with a new package.) Add the egg and whisk thoroughly. Scrape the yeast mixture into the refrigerated dry mixture and stir to moisten the flour. There will still be some drier bits of dough; that’s fine. Cover the dough with plastic wrap and chill overnight.
3. The next day, take the dough out of the refrigerator and scrape it onto a well-floured surface. It will be quite rough, but don’t worry; it will come together as you work with it.
4. Flour the top of the dough and use your hands to shape the dough into a rough square, pressing the loose bits together as you go. Using a rolling pin, roll the dough into a rectangle about 9 inches by 15 inches, keeping the longer side parallel to your body.
5. For the first turn, fold the rectangle of dough into thirds like a letter. Then turn the dough to the right once, so that the long edge of the dough is parallel to your body and the seam is at the top. As the dough is still quite rough, a metal bench scraper will help you lift the dough to make these folds.
6. Flour the surface and the dough and repeat the step above two more times, for a total of three turns. As you do the turns, the dough will become more cohesive and streaks of butter will begin to show throughout. The dough will also soften as the butter begins to warm and the yeast begins to react.
7. To shape the dough, cut it in half with a knife or a bench scraper. Roll each piece of dough into a 12-by-8-inch rectangle, keeping the shorter side parallel to your body. Rub the softened butter over the rectangles, dividing it equally between the two. Sprinkle the sugars evenly over the butter.
8. Roll up the dough, one rectangle at a time, starting at the shorter edge closer to you and keeping a tight spiral as you roll. Slice each log into 6 even slices and lay them on 2 buttered baking sheets, spiral side up, 6 to a sheet.
9. To proof, cover each baking sheet with a towel or plastic wrap and allow to rest in a warm area for 2 hours. While the dough is proofing, preheat the oven to 425°F. After 2 hours, the spirals will be slightly swollen but will not have doubled in size.
10. Bake for 15 to 18 minutes, rotating the sheets halfway through. The pastries are ready to come out of the oven when the sugars are caramelized and the tops of the Danish are golden-brown. These pastries are best eaten the day they’re made, ideally within the hour.