For the dough: Stir together the water, yeast and granulated sugar in a spouted measuring cup. Let sit until the yeast is foamy, about 5 minutes.
Combine the salt, cardamom and 3 1/2 cups flour in the bowl of a stand mixer fitted with the paddle attachment and mix briefly on low speed to combine. Beat together the 1 egg, 3 yolks, honey and oil in a medium bowl. Stir in the yeast mixture. Add the wet ingredients to the flour mixture, mixing on low speed until combined. Add 1 more cup flour and mix on medium speed to make a sticky dough that comes together in a loose mass around the paddle. Switch to the dough hook and knead on medium speed to make a smooth but still somewhat sticky dough that clears the sides of the bowl, adding up to 1/2 cup more flour if necessary, about 4 minutes.
Dump the dough onto a floured work surface and knead by hand a few times to make a smooth ball. Oil a large bowl and turn the dough ball in the oil to coat it. Cover with plastic wrap and let rise in a warm place until doubled in size, about 1 hour.
For the filling and glaze: Meanwhile, stir together the jam and cardamom in a small bowl.
Shape the dough: When the dough has risen, punch it down and divide it into 4 equal pieces. Line an unrimmed baking sheet with parchment paper.
Form the dough pieces into balls on a floured work surface. With a lightly floured rolling pin, roll one ball into a 10-inch circle and place on the prepared baking sheet. Spread with a third of the filling, leaving a 1-inch border all around. Roll out another dough disc in the same manner and place on top of the first; top with the second third of filling. Repeat with a third dough disc and the remaining filling. Roll out the remaining dough disc and place it on top of the last layer of filling.
Center the bottom of a small drinking glass (about 2 inches in diameter) in the middle of the dough to mark the center. At the 12 o'clock mark, cut through the dough with a very sharp knife from the edge of the glass to the edge of the dough circle, leaving the dough underneath the glass uncut. Repeat at the 3 o'clock, 6 o'clock and 9 o'clock points on the circle to make 4 quarters. Cut through the middle of each quarter in the same manner to make 8 equal wedges. Cut through each wedge one more time in the same manner to make 16 wedges.
Remove the drinking glass. Lift the edges of 2 wedges that are next to each other and twist them away from each other twice, then pinch the ends together to reconnect them and make a pointed tip. Repeat with the remaining pairs of wedges. Cover the dough with oiled plastic wrap and let rise in a warm place until doubled in size, about 45 minutes.
Position an oven rack in the center of the oven and preheat the oven to 350 degrees F. Beat the egg yolk and 2 tablespoons milk in a small bowl. Brush the egg wash all over the risen dough. Pinch the points again to reshape if the dough has risen so much that the points no longer look pointy. Bake the bread until puffed and golden brown, about 30 minutes. Cool on a rack until just warm, about 30 minutes.
Stir together the confectioners' sugar, lemon juice and 2 tablespoons milk in a small bowl, adding up to 1 tablespoon more milk or confectioners' sugar if needed so that the glaze is the correct consistency to slowly drizzle off the end of the spoon. Drizzle the glaze all over the bread and let harden, about 30 minutes. Serve warm or at room temperature.
When measuring flour, we spoon into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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