To make the dough, in a 1-quart liquid measuring cup or medium bowl, whisk the eggs plus yolks, milk, yeast and vanilla. In a stand mixer with the dough hook, mix the flour, sugar and salt on low until combined, about 30 seconds. With the mixer running, slowly add the egg mixture, then knead on medium until a wet, slightly lumpy dough forms, about 2 minutes, scraping the bowl once or twice.

With the mixer running on medium, add the butter 2 pieces at a time, mixing for about 30 seconds after each addition. When all the butter has been added, scrape the bowl and mix on medium until the dough is smooth, elastic and pulls away from the sides of the bowl, 7 to 9 minutes. If the dough is too sticky to clear the sides of the bowl, mix in up to 2 tablespoons flour, kneading for about 2 minutes after each addition. Scrape the sides of the bowl and gather the dough in the center. Cover with plastic wrap and let rise at room temperature until just shy of doubled, 30 to 45 minutes, then refrigerate for at least 6 hours or up to 24 hours.

When you are ready to shape the dough, make the filling. In a small saucepan, combine the butter and milk. Bring to a simmer over medium, stirring; when the butter is melted, remove from the heat and cool for a few minutes. In a medium bowl, whisk the sugar, cocoa, espresso powder and salt. Whisk in the milk-butter mixture until almost smooth; it’s OK if tiny lumps remain. Add the tahini and whisk until smooth, then whisk in the vanilla; set aside.

Butter two 9-by-5-inch loaf pans, then line each with an 8-by-14-inch piece of kitchen parchment, allowing the excess to overhang the long sides of the pan; set aside.

Remove the dough from the refrigerator. Lightly flour the counter and turn the dough out onto it. Using a chef’s knife or bench scraper, divide it in half; each piece should weigh about 540 grams (19 ounces). Return 1 piece to the bowl; re-cover and refrigerate. Using your hands, form the remaining piece into a rough 6-by-8-inch rectangle. Using a rolling pin, roll it into a 12-by-18-inch rectangle with a long side nearest you (it’s OK if the rectangle does not have perfectly squared corners); lightly dust with flour as needed to prevent sticking.

Using an offset icing spatula, spread half of the chocolate filling in an even layer over the dough, leaving a 1-inch border on the long side farthest from you. Sprinkle the filling evenly with half of the chopped chocolate. Starting with the side closest to you, roll the dough into a tight cylinder; pinch the seam to seal. Roll the cylinder onto its seam and, using your hands, gently roll it back and forth against the counter to extend its length to about 18 inches; if any sections are thicker than others, apply more pressure to those areas when rolling to even them out. Cover the cylinder with a kitchen towel. Remove the second portion of dough from the refrigerator; roll it out, spread on the remaining filling, sprinkle with the remaining chopped chocolate and form the dough into an even cylinder as you did the first portion; cover with another towel.

Place the first cylinder seam side down on a large cutting board. Using a chef’s knife and starting at one end, cut the cylinder in half lengthwise; slice straight down and use firm, even pressure (do not use a sawing motion). You will have two rope-like pieces with cut sides that expose the layers of filling and dough. With ropes positioned perpendicular to the counter’s edge and the cut sides facing up, cross them at their midpoints, forming an X.

Starting at the center of the X, where the ropes meet, form the sections of the ropes closest to you into a twist by passing one under the other, always keeping the cut sides up; you should get in 3 to 5 twists. Pinch the ends together to seal. Repeat with the ropes on the other side of the X. Using your hands, shorten and compact the loaf by gently and simultaneously squishing both short ends together until the loaf measures about 9 inches. Transfer to a prepared pan and cover loosely with a towel. Shape the second cylinder in the same way and cover. Let rise at room temperature until doubled, 1 to 1½ hours.

Meanwhile, make the syrup. In a small saucepan, combine the sugar, espresso powder and ¼ cup water. Bring to a simmer over medium, stirring occasionally to dissolve the sugar. Remove from the heat and set aside. Heat the oven to 350°F with a rack in the middle position. Cut two 9-by-12-inch pieces of foil.

Uncover the loaf pans and place them, spaced about 3 inches apart, on a rimmed baking sheet. Place the baking sheet in the oven and bake until golden brown, about 30 minutes. Working quickly, rotate the baking sheet 180 degrees and lay a piece of foil over each loaf. Continue to bake until the centers reach 190°F to 200°F, about another 10 minutes.

Set the baking sheet with the loaf pans on a wire rack. Brush the top of each warm babka with 1 to 2 tablespoons syrup. Cool for 30 minutes, then, using the parchment slings, lift the babkas from their pans and set them directly on the baking sheet. Peel back the parchment on the sides and brush all sides with the remaining syrup. Cool completely, then remove and discard the parchment.

Cinnamon-Walnut Babka: Follow the recipe to make the dough and prepare the pans. When you are ready to shape the dough, make the filling: In a medium bowl, whisk together 199 grams (1 cup) packed brown sugar, 1 tablespoon ground cinnamon, 1 tablespoon grated orange zest and ¼ teaspoon table salt. Add 57 grams (4 tablespoons) salted butter (cut into 3 or 4 pieces, room temperature) and, using your fingertips, rub the butter into the spiced sugar until the mixture resembles wet sand. Cover and set aside at room temperature. Have ready 110 grams (1 cup) walnuts (toasted and finely chopped). Follow the recipe to divide the dough, then roll out and fill each portion as directed, sprinkling half of the butter-sugar mixture on each rectangle, then evenly sprinkling half of the walnuts onto the butter-sugar layer. Form the dough into cylinders of even thickness, cut the cylinders and shape the loaves as directed, then cover and let rise. While the loaves rise, make the syrup: In a small saucepan, combine 71 grams (⅓ cup) white sugar, ¼ cup water and three 3-inch strips orange zest. Bring to a simmer over medium, stirring occasionally to dissolve the sugar; remove from the heat and set aside. Follow the recipe to bake the babkas and brush with syrup, removing and discarding the orange zest from the syrup before use.