Make the dough: Follow the directions for Danish Dough, up to and including fold no. 3. The dough should be chilled and ready to use.
Make the filling: In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, sugar, salt, and cardamom on medium for 1 to 2 minutes, until everything is well incorporated; it should be smooth and creamy. Set the filling aside at room temperature to keep it soft and spreadable.
Generously butter a 12-cup muffin tin.
Lightly dust a work surface with flour. Roll the dough out into a 13 by 18-inch rectangle. Spread the cardamom filling evenly across the entire surface of the dough.
Roll the dough up widthwise, like a jelly roll, as tightly as possible. Make twelve shallow cuts at 1-inch intervals and cut the roll into slices.
Place each piece into a buttered cup of your muffin tin, with one of the cut sides down.
Cover the muffin tin with a kitchen towel and set them in a warm area until they are noticeably puffier, 1 to 2 hours.
Preheat the oven to 375°F (190°C).
Place the muffin tin on a larger baking tray before baking. Bake for 25 to 30 minutes, until the pastry looks dark golden brown.
Let the buns cool for 2 to 3 minutes, then tip the muffin tin onto its side and use an offset spatula to gently pry each bun loose.
Roll the surface of each morning bun in the cardamom sugar.
