Kardemummabullar: Swedish Cardamom Buns

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1. 1Step 1: In the bowl of a stand mixer fitted with a dough hook, combine the yeast, sugar, milk, egg, melted butter, flour, cardamom, and salt. Knead on medium speed until the dough is smooth, tacky, and can be stretched into a thin sheet without tearing easily, 20 to 25 minutes depending on your mixer (see note).
2. 2Step 2: Cover with plastic wrap or a clean kitchen towel and let rise in a warm spot until doubled in size, about 1 hour. (Alternatively, refrigerate overnight for a slow rise.)
3. 3Step 3: Meanwhile, make the filling by mixing the butter, sugar, vanilla, and salt until smooth. For the cardamom sugar, combine the sugar with the ground cardamom.
4. 4Step 4: On a lightly floured surface, roll the dough into a 12x24-inch rectangle with the short side facing you. Spread the filling evenly over the dough, then sprinkle generously with the cardamom sugar (reserving some for finishing).
5. 5Step 5: Fold the top edge down two-thirds of the way, then fold the bottom edge up over the top, like folding a letter. Roll out again into a 12x14-inch rectangle to help the layers stick and to lengthen the strips.
6. 6Step 6: Cut into 12 strips, each about 1 inch wide. Twist each strip tightly, then coil it into a knot, tucking the end into the center. Cover and let rise until puffed, 30 to 45 minutes.
7. 7Step 7: Preheat the oven to 350ºF/175ºC. with a rack in the center. Line a rimmed baking sheet with parchment paper. Brush the buns with egg wash, then bake until golden brown and a thermometer inserted in the center registers 190ºF (87ºC), 22 to 25 minutes.
8. 8Step 8: While cooling, make the syrup. Heat the water and sugar in a small pot until the sugar is dissolved. Brush each bun generously with syrup, then sprinkle with the remaining cardamom sugar.