If using active dry yeast, heat the milk in the microwave or on the stovetop until it is “fingervarm” (finger warm), meaning it should feel warm to the touch but not hot. Add your yeast, a small amount of the sugar needed for the recipe, stir, and leave it for 5-10 minutes until the mixture starts to bubble up. If using instant yeast, simply add the yeast to the lukewarm milk – there usually is no need to wait for it to bubble up, but follow the instructions on your package of yeast if in doubt!
Combine the egg, egg yolk, remaining sugar, vanilla extract, cardamom, and salt in a large bowl, or the bowl of a stand mixer. Mix well.
Add the milk and yeast mixture to the egg mixture and whisk or stir to combine.
Add in the flour, stirring with a wooden spoon or using the dough hook on the stand mixer.
Once the dough starts to come together into a scraggly dough, add in the softened butter as well.
Knead until smooth and elastic, probably around 5-10 minutes. Add flour a bit at a time if the dough sticks to your hands or the surface. If you prefer not to get your hands messy, feel free to use a stand mixer for this step (with the dough hook attachment). 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.
While the dough is rising, make the filling. Combine softened butter, brown sugar, cardamom, and salt and stir together until you get a smooth paste. Set aside until the dough is ready.
Once your dough has doubled in size, turn out onto a clean work surface and press into a rough rectangle shape.
Roll the dough out into a rectangle that is about a quarter of an inch (0.5cm) thick (corresponds to a rectangle about 12" by 17").
Spread your filling evenly on the top half of the dough.
Fold the bottom half of the dough over the top with the filling.
Cut into 12 equal sized strips, about 1 inch in width.
Pick up a strip of dough and hold it with your index, middle finger, and thumb in your left hand.
Twist each strip clockwise with your right hand gently, as much as it will allow.
Wrap the twisted dough strip counter-clockwise around the two fingers of your left hand that are holding the strip. You should be able to wrap the dough around your fingers twice.
Tuck the end of the strip through the middle. Try to press the ends together so they stay in place.
Place the roll on a baking sheet lined with parchment paper. Repeat with the rest of the dough. We use two baking sheets with six buns on each sheet.
Cover the buns loosely with cling film or a clean dishtowel and let them rise another 45 minutes. In the meantime, preheat your oven to 375 degrees F (190 degrees C).
Once the buns have finished proving (try poking the dough; if it leaves an indent that doesn't spring back immediately, they should be ready!), you can tuck in any ends that may have unraveled during the second prove. 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 buns.
Sprinkle with pearl sugar (alternatively, use turbinado sugar, raw sugar, or just regular sugar).
Bake for 10-12 mins, or until golden brown on top. You can bake both sheets at once or bake them one at a time in the center of the oven. Just be aware of how your oven may differ from the top to the bottom if you choose to bake them at the same time; for example, our oven is much hotter on the bottom, so we switch the baking trays about halfway to prevent too much browning on the bottom tray.
Once done, let them cool on a cooling rack; enjoy the buns with coffee or tea!