Make the dough: Put the flour, lemon zest and butter in the bowl of a standing mixer set with a dough hook. Mix on medium-low speed until the ingredients are well combined and the butter pieces are no larger than a small pea, 1 to 2 minutes.

In a small bowl, mix the yeast, milk, and sugar together, stirring until the yeast dissolves. Add the yeast mixture to the flour mixture and mix on low speed until the liquid is incorporated, stopping the mixer and scraping the ides and bottom of the bowl as needed to ensure that all the flour is moistened. The dough will still be slightly dry and shaggy.

With the mixer running on low, gradually add the wine and mix until the dough absorbs the liquid, another minute or two. Add the egg, egg yolk, and salt and mix on medium-low speed until the dough is smooth and homogenous, 5 to 7 minutes.

Transfer the dough to a large bowl and cover with a towel. Set it in a warm place and let rise until doubled in size, 40 to 60 minutes.

While the dough is rising, make the poppyseed filling: Combine the ground poppy seeds, milk and sugar in a small saucepan and bring the mixture to a lively simmer over medium-high heat, then cook, stirring constantly, until the mixture becomes thick and spreadable, about 20 minutes. Remove the pan from the heat, stir in the vanilla, and set the filling aside to cool for about 10 minutes (if the filling is too warm, the egg white will set when you add it.)

Add the egg white to the filling and stir to combine well. Set aside to cool completely, about 20 minutes.

Meanwhile, make the walnut filling: Pulse the walnuts in a food processor until finely ground (don't grind so much that they become a paste). Transfer the walnuts to a medium bowl, add the milk, sugar, lemon zest, vanilla, brandy, if using, and egg white, and stir until combined into a spreadable paste. Set aside.

Line two baking sheets with parchment paper and set aside.

Shape the beigli: Once the dough has doubled in size, transfer it onto a clean work surface. Knead it a few times and divide it into 2 equal pieces. Roll out one piece of dough on a lightly floured surface with a rolling pin to a 14-by-11-inch rectangle. Turn the dough if necessary so a short end is in front of you. Spread the walnut filling evenly over the dough, leaving a ¾-inch border without filling on the long sides of the dough and a slightly larger border along the short end farthest from you. (The filling will be pushed toward the end as you roll up the dough, so this wider border will prevent it from leaking out when you shape the roulade.)

Fold the right and left sides of the dough inward about 1 inch over the filling. (This will prevent the filling from seeping out the sides of the beigli.) Starting at the end closest to you, roll up the dough into a log shape. Transfer the beigli to one of the prepared baking sheets, seam side down; set aside. Repeat the process with the second piece of dough and the poppy seed filling and place the poppy seed beigli on the second baking sheet. Let the pastries rest for 15 minutes.

Place the racks in the upper and lower thirds of the oven and preheat the oven to 400°F.

Brush the pastries with the egg wash and poke several holes along the tops and sides of the rolls with the tines of a fork. This will allow steam to escape during baking. Bake the pastries for 15 minutes, then reduce the oven temperature to 375°F. Rotate the pans front to back and top to bottom and continue baking until the pastries are a deep golden brown, 20 to 30 minutes. Take the beigli out of the oven and cool for at least 20 minutes, or until completely cool.

With a serrated knife, cut the beigli into 1-inch slices. Serve at room temperature.