In a small saucepan over medium heat, melt the butter. Stir in the milk and let warm until it reaches 90-110 degrees F (or the temperature listed on the package). A thermometer is helpful.
Pour a small amount (about 3 tablespoons) of the butter and milk mixture into a small bowl. Stir in the yeast and let sit for 3-5 minutes, until bubbles start to form. Use a little spatula to scrape down the sides.
In a large bowl or the bowl of a standing mixer fitted with the dough hook attachment, combine flour, sugar, cardamom, and salt. Add the yeast mixture and the rest of the milk and butter mixture. Combine with the standing mixer set to medium speed or using a wooden spoon. Continue kneading the dough with the dough hook attachment until it releases from the sides and is smooth and elastic, about 1 minute. If using your hands, transfer to a lightly floured surface and knead by hand for 3-4 minutes.
Leave the dough in the bowl, (or place the dough back in the bowl), cover with a tea towel, and let rise until doubled in size, this could take anywhere from 30-60 minutes depending on the temperature of your kitchen and the quality and quantity of the yeast.
Place 30-34 paper muffin liners on the rimmed baking sheets. (See recommendations in blog post).
When the dough has finished rising, transfer it to a lightly floured counter surface. Knead it for a minute or two and then cut it into half. Roll out each half into a large rectangle, about 10-12 inches by 16-18 inches.
With the shorter side of the rectangle facing you, use a small spatula to spread half of the softened butter onto the rolled out dough. Next, sprinkle with half of the sugar and half of the cardamom. (Add more or less butter, sugar, and spice as desired).
TO MAKE TWIRLS: With the short side facing you, fold the dough in half and cut into 15-17 pieces. Use a pastry slicer or knife and start in the middle and then keep dividing each section in half. (See image). Next, pick up one strip at a time. Hold at each end and twist and twirl one side around the other, tucking the final end piece underneath and placing it one of the muffin liners on the baking sheet. Repeat with each strip. TO MAKE ROLLS (easier!): Roll up the dough and then slice into 15-18 pieces.
Roll out the second piece of dough, top with butter, sugar, and cardamom, and shape as desired per directions above.
Once all the buns are on the baking sheets. Cover with a tea towel and let rise for about 30-40 minutes, until you see they have risen a bit more.
Meanwhile, preheat the oven to 425 degrees F.
One the buns are done rising, brush with the beaten egg and then sprinkle with pearl sugar. Bake for 8-9 minutes, until golden brown. (Monitor oven closely as cooking time can vary.)
Once done, transfer to a wire rack to cool slightly. Enjoy! These are best when fresh, so freeze leftovers once fully cooled and take them out as needed.