MAKE THE DOUGH
In a small bowl, combine warm milk and yeast. Let it sit for about 5-10 minutes until frothy.
In a large mixing bowl, combine flour, salt, and sugar. Make a well in the center and add the activated yeast mixture, softened butter, and egg.
Mix everything until a dough forms.
Knead the dough on a floured surface for about 5-10 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a kitchen towel, and let it rise in a warm place for about 1-2 hours, or until doubled in size.
MAKE THE FILLING
In a small bowl, mix together softened butter and vanilla extract until well combined.
In another bowl, mix together granulated sugar and ground black cardamom until evenly combined.
SHAPE THE BUNS
Once the dough has doubled in size, punch it down to release the air.
Roll out the dough on a floured surface into a large rectangle, about 1/4 inch thick.
Spread the butter and vanilla mixture evenly over the dough.
Sprinkle the sugar and cardamom mixture evenly over the buttered dough.
Fold the left and right sides of the dough inward to overlap on top of each other to create three layers.
Roll out the folded dough a bit to flatten it slightly.
Cut the dough into long strips, about 3/4 inches wide.
Take each strip and stretch it out slightly.
Wrap each strip around your fingers twice to create a twisted shape, then wrap it around the center and tuck the end underneath to secure the design.
SECOND PROOF
Place the shaped buns on a baking sheet lined with parchment paper, leaving some space between each bun.
Cover the buns with plastic wrap and a kitchen towel and let them rise again for about an hour in a warm place, or until they are puffy.
Meanwhile, preheat your oven to 375°F (190°C).
SIMPLE SYRUP & TOPPINGS
In a pot over medium heat add the water, sugar, and vanilla extract.
Bring to a boil so all the sugar is dissolved and then reduce the heat to low and simmer for 10 minutes. Transfer to a bowl and allow to cool to room temperature so it thickens up a bit more.
In a small bowl, whisk together the egg and milk to make an egg wash.
In another bowl, mix together granulated sugar and ground cardamom.
BAKE
Brush the risen buns with the egg wash.
Bake in the preheated oven for 15-20 minutes, or until golden brown and cooked through.
Brush the cardamom buns with simple syrup and sprinkle the tops with white sugar and black cardamom.
Let the buns cool slightly before serving and enjoy your delicious Swedish cardamom buns!