Feed sourdough starter 4-12 hours before starting this recipe. You want the starter to be active, bubbly, and at its peak.
Add unsalted butter, water, active and bubbly sourdough starter, salt, sugar, flour, and egg to the bowl of a stand mixer.
With your dough hook, mix on low speed until smooth and glossy.
Being a wet, sticky dough, this could take 10-15 minutes. If longer, I'll often give my mixer a rest, as it can get pretty warm by this point.
Refrain from adding more flour, even though the dough might seem to need it. When the dough is ready, it will pull away from the sides of the bowl and will also pass the windowpane test.
Cover the dough with plastic wrap or a damp towel and rise for 6-8 hours or until doubled in size. This may take longer if your home is pretty cool.
After this first rise, we want to refrigerate the dough so that it stiffens up for shaping. This can be for 2-3 hours if you're ready to bake the same day, or you can leave the dough in the refrigerator overnight.
You'll want to take it out about 5-10 minutes before filling and shaping so that it softens up enough to work with, while still being cool enough to hold shape.
Mix together the softened butter, brown sugar, cardamom and cinnamon.
Roll out your dough to a 14" by 20" rectangle.
Spread your filling on the bottom half of the dough - the half that will measure 7" by 20".
Fold the unfilled half of the dough over the filled half, leaving your dough measuring 7" by 20", and lightly pressing the edges.
Cut the dough into 7" long strips; you should have around 12 total. I like to use a pizza cutter for this, but a sharp knife will also work.
At this point, there are lots of shaping options: you can simply roll up these strips like typical cinnamon buns, or twist and roll each strip, or slice the single strips of dough into two strips each that are then separately twisted and rolled together much like a soft pretzel.
Using a bench scraper, carefully place buns on a baking tray lined with parchment paper. Space them out to allow for the rise.
Lightly cover and start your second rise in a warm place until doubled. This could be a couple of hours, or even overnight, depending on temperature.
Preheat your oven to 400 degrees.
Bake for 18-20 minutes or until golden brown.