In a small bowl, sprinkle the yeast over the lukewarm milk. Stir to combine and allow to sit until frothy, about 10 minutes.
In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour, sugar, cardamom, and salt.
Mix in the milk with the yeast, followed by the butter to form a dough. On a lightly floured surface, knead until smooth and soft. Place back in the bowl, cover with a towel or plastic, and allow to rise until doubled, about 1 hour.
To make the cinnamon filling:
In a medium bowl, mix together the softened butter, sugar, and cinnamon until smooth.
Preheat oven to 400˚F. Line two baking sheets with parchment or lightly grease.
On a lightly floured surface, roll the risen dough into a rectangle about 24 inches long and 18 inches wide. Cover in an even layer with the cinnamon sugar filling. Roll up the dough, short end to short end to form a log. Pinch together the end to seal.
Cut the log into rolls about 1 inch thick with a sharp knife. Arrange the rolls on the prepared baking sheets about 2 inches apart. Cover with a towel and allow to rise until puffed, about 30 minutes.
Brush the tops of the rolls with the beaten egg. If using pearl sugar, sprinkle over the brushed rolls and bake in the preheated oven until golden, 12-14 minutes. Transfer the cooked rolls to wire racks to cool.
If topping with a glaze: In a medium bowl, whisk the water into the powdered sugar to create a smooth glaze. If too thick, add a little more water. If too thin, add a little more powdered sugar. If desired, mix in a little cocoa powder to make the glaze chocolate. Drizzle the glaze over the cooled rolls, either a dollop in the center or around in a swirl.
These Kanelsnegle are best the day they are baked.