In a medium-sized bowl, mix the active sourdough starter with cold milk, flour, and sugar. Cover and let it rise in a warm spot for about 4 hours or until the levain has doubled or tripled in size.

Gather all the ingredients. Add everything except the butter to the bowl of your stand mixer fitted with a dough hook. Mix on medium speed until the dough comes together. Cover the bowl and let the dough rest (autolyse) for 30 minutes.

Restart the mixer and knead the dough on medium speed for 5-10 minutes.

Gradually add the softened butter, one cube at a time, until all is incorporated.

Continue kneading at medium speed for 15-25 minutes until the dough passes the window-pane test.

Transfer the dough to a clean bowl and let it proof in a warm spot, ideally at around 78°F (26°C), for two hours.

After two hours, move the dough to the refrigerator to cold-proof for at least six hours.

Combine the softened butter, brown sugar, and ground cardamom in a bowl. Mix with a fork until it forms a spreadable paste. Keep at room temperature until ready to use.

Transfer the cold dough to a lightly floured work surface. Let it sit at room temperature for 10-15 minutes if it's too stiff to roll out.

Roll the dough into a 19x12 inch (50x30 cm) rectangle using a rolling pin.

Spread the cardamom filling evenly over the dough with an offset spatula.

Fold one long side of the rectangle down to cover 2/3 of the dough, then fold the other long side over the top.

Use a rolling pin to even out the dough.

Cut the dough into 12 strips, each about 1.5-2 inches wide.

Split each strip into three sections, leaving one end joined. Braid the sections to form a three-stranded plait, then roll up the braid to form a bun. Place the shaped buns in a greased muffin tin.

Cover the muffin tin loosely with cling film and let the buns proof at around 78°F (26°C) for 9-12 hours until doubled in size.

Preheat your oven to 355°F (180°C). Bake the buns for 18-20 minutes until they turn golden brown.

While the buns are baking, prepare the brown sugar glaze: combine the ingredients in a small pot and heat over medium heat until the sugar dissolves.

Once the buns are out of the oven, brush them immediately with the glaze using a pastry brush. Transfer the buns to a cooling rack and let them cool for 20-30 minutes before serving.