How to Make It
Make the shortcrust. Place the sugar, flour, baking powder, butter, and egg yolk in a bowl and quickly knead together until well combined. Shape into a disk and set aside. This dough can be made up to a day in advance, wrapped in plastic wrap, and refrigerated, but it should be brought to room temperature before combining it with the yeast dough.
Make the yeast dough. If using fresh yeast crumble the fresh yeast into a large mixing bowl and sprinkle with the salt and sugar. Set aside for 10 minutes. Stir in the water and vanilla extract; add the butter, egg, and flour and stir. (If using instant yeast, simply stir all the dough ingredients together and proceed immediately to the kneading phase.) Dump the shaggy dough out onto a lightly floured work surface and knead until smooth and elastic, about 3 minutes. Resist adding too much more flour as you knead; the dough should remain as soft as possible.
Roll out the yeast dough to about 1-inch thickness and place the disk of short crust on top of the dough. Fold the yeast dough over the short crust and knead together by hand until fully combined, about 2 minutes. Shape into a ball, place in a bowl, and cover with a clean dishcloth. Set in a warm, draft-free spot to rise for 1 hour.
Make the filling. Mix the ground poppy seeds, sugar, semolina, and salt in a saucepan. Add the butter and milk. Place the pot over medium-high heat and, stirring constantly, bring to a boil. Immediately remove from the heat and set aside to cool. Once the mixture is lukewarm, stir in the egg, vanilla extract, and rum. Set aside.
Line a baking sheet with parchment paper. After the dough has proofed, divide it in half and set one piece aside. Roll out the other half to a 12- by 14-inch rectangle. Spread the dough evenly with half of the poppy-seed filling, leaving no border. Starting from one of the long sides, roll up the dough tightly. Transfer the dough to the prepared baking sheet. Repeat with the second piece of dough and the remaining filling.
Hold a pair of kitchen shears perpendicular to one loaf, 1 inch from the top of the roll, and snip the dough almost all the way through, leaving about 1 inch of the dough uncut, which will function as a hinge. Repeat, moving down the loaf, at 1-inch intervals. When finished, set aside the shears and, using your fingers, gently separate and twist out each snipped segment, alternating to the left and right of the roll, so that the cut sides of each segment face upward. Tug gently at the segments so that each segment on the left side of the loaf slightly overlaps with the one in front of it, and the same on the right. Repeat with the second loaf. Cover the baking sheet with the dishcloth and set the loaves aside to proof for 30 minutes.
Preheat the oven to 400°F.
Remove the dishcloth and place the baking sheet in the oven. Bake for 40 minutes, or until the loaves are a deep golden brown. You may need to cover them with a piece of aluminum foil in the last 10 to 15 minutes of baking. Remove the baking sheet from the oven and place on a rack to cool.
Make the glaze. When the loaves have fully cooled, whisk together the confectioners’ sugar and water until completely smooth. Brush the glaze thinly over the loaves. Let the glaze set before serving. The Mohnzopf is best served the day it's made, but it can be kept for an additional day by wrapping it tightly in plastic wrap