In the bowl of a stand mixer fitted with a dough hook attachment, add all the dough ingredients. Knead for 20–25 minutes or until you can stretch a small piece of dough into a thin, translucent film (windowpane test). The dough should be well-hydrated, silky, and smooth but not sticky.
Wrap the dough in plastic wrap, forming a rectangle, and place it in the fridge for 30–40 minutes or until cold. Prepare two baking sheets lined with parchment paper.
Meanwhile, prepare the filling. In one bowl, whisk together the sugar and ground cardamom. In another bowl, whisk the butter until soft and easily spreadable.
Remove the dough from the fridge and place it on a lightly floured surface with the short side of the rectangle facing you. Roll it out into a 14 x 18-inch (35 x 45 cm) rectangle, about ⅕ inch (5 mm) thick.
Spread the butter evenly over the dough, then sprinkle the cardamom sugar on top in an even layer.
Grab the bottom third of the dough and fold it over the middle third. Then, fold the top third over the previous fold (this is called a letter fold).
Roll the dough slightly to widen it and seal in the filling.
Using a pizza cutter or a long knife, cut the dough into 15 strips, each about 1 inch (2.5 cm) wide.
Take one strip and gently stretch it to elongate it. Twist it 2-3 times, then coil it into a spiral bun, tucking the loose end underneath. Place the bun on a prepared baking sheet and gently press it to secure the tail, preventing it from unraveling during proofing and baking. Repeat with the remaining strips. When arranging the buns on the baking sheet, leave some space between them—I usually place a maximum of eight buns per sheet.
Cover the trays with plastic wrap and let the buns proof for 1.5–2 hours or until puffy. Do not proof them in the oven with the light on, as the butter filling may melt and leak out.
Once the buns have risen and look puffy, brush them with the egg wash. Bake one tray at a time in a preheated oven at 425F (220C) for 10–12 minutes or until golden brown.
Remove from the oven and allow to cool before serving.