In a small bowl, combine warm milk, 1 tsp granulated sugar and yeast. Allow to sit for about 5-10 minutes until foamy.
In a bowl of a stand mixer fitted with a whisk attachment, add eggs, salt and brown sugar and mix on medium speed until combined, about 1 minute. Change attachment to the dough hook.
Add in flour, ground cardamom, and yeast mixture to the egg mixture. Mix on medium-low speed until dough starts to come together. Increase speed to medium and slowly add in very soft butter, 1 tablespoon at a time. Allow the dough to knead on medium speed for 8 minutes.
Remove dough from bowl and place on a lightly floured surface. Dough will be fairly loose and sticky. Gently shape into a ball and place seam side down into a large bowl that has been buttered. Cover and allow to proof for 2 hours or until at least doubled in size.
While the dough proofs, make the filling. Combine brown sugar, cardamom and salt in a small bowl and stir with a spoon until well mixed.
Line a large baking sheet with parchment paper and set aside.
Once the dough has risen, remove from bowl and place onto a lightly floured surface. Using a rolling pin, roll the dough into a 16X12 rectangle (with the shorter side in front of you). Using an offset spatula spread very soft butter into an even layer over the dough, leaving a 1-inch border on the top end. Sprinkle evenly with sugar mixture. Starting at the short end nearest you, roll the dough up tightly into a cylinder. Pinch the seam closed and turn the dough over so that it is seam side down.
Trim off the ends of the dough if uneven. Cut into 12 even slices. Place the rolls onto prepared baking sheet at least 2 inches apart with the swirl facing up. Cover with plastic wrap and allow to proof one last time for 45 minutes.