Heat up the milk, either in the microwave or in a saucepan, until it is “fingervarm” (finger warm), meaning it should feel warm to the touch but not hot. You don’t want to kill the yeast! Add the yeast and stir to dissolve. Let it rest 5-10 minutes until it begins to froth and bubble a little bit. (If your yeast doesn’t do anything, it may be expired. Check the expiration date on the package and start over with new yeast!)
Combine the egg, egg yolk, sugar, vanilla extract, cardamom, and salt in a large bowl. Mix well.
Add the milk and yeast mixture to the egg mixture and whisk to combine.
Slowly add the flour, stirring with a wooden spoon. Once the dough starts to come together, you can start kneading.
Add the softened butter and knead until smooth and elastic, probably around 5-10 minutes. Add a bit of flour if the dough sticks to your hands or the surface. If you prefer not to get your hands messy and covered in butter, feel free to use a stand mixer for this step. The texture of your dough before its first rise should be soft and smooth, not sticky and not too dry.
Cover and let your dough rise for about 45 minutes, or until doubled in size.
For the filling, combine softened butter, brown sugar, cinnamon, and salt and stir together until you get a smooth paste.
Once your dough has doubled in size, roll it out into a rectangle that is about a quarter of an inch (0.5cm) thick.
Spread your filling evenly on top and then section your rectangle into four equal strips.
Roll each strip (from the long side) so you have a log with a swirl with 1.5 revolutions.
Divide each log into 12 pieces and cut them - you will have around 48 pieces in total.
Place your pieces on a baking sheet lined with baking paper. Cover the pieces with cling film or a clean dish towel and let them rise for about 45 minutes in a warm place. In the meantime, preheat your oven to 350 degrees F (175 degrees C).
Make your egg wash (1 egg whisked together with a splash of water until there are no more gloopy streaks of egg white), then brush over the pieces and bake for about 15 minutes. They may be a little bit lighter in color when they are done than normal cinnamon rolls - make sure you check if they are done by trying one! It can be easy to overbake since the pieces are small. Once they are done, let them cool, then eat!