In a stand mixer bowl with the dough hook, combine yeast, a bit of sugar, and warmed milk. Let it sit for 5-10 minutes until frothy.
Add remaining sugar and softened butter. Mix until the butter is in chunks. Add beaten eggs, vanilla, and orange zest; mix until combined.
Whisk together flour, cinnamon, cardamom, and salt. Slowly add the flour mixture 1/2 cup at a time until incorporated.
Set the mixer to medium speed and knead until a smooth mass forms. Adjust with more flour if needed. Knead for 5 minutes.
Remove the dough, knead by hand for 2 minutes, place in a greased bowl, and let it rise for 1 1/2 – 2 hours until doubled.
For the filling, beat together butter, brown sugar, cinnamon, and cardamom. Add flour and beat until combined.
Roll out the dough into a 10x16 inch rectangle. Spread the filling, leaving a 1-inch border. Roll it up jelly-roll style.
Place the log on a parchment-lined baking sheet, seam side down. Cut into 16 rolls without fully separating.
Turn each roll to form a wreath shape. Use a ramekin in the center to hold the shape.
Let it rise for 30 minutes. Preheat the oven to 350˚F.
Bake for 25-30 minutes until golden brown. Cool for 5-10 minutes, then drizzle with icing. Enjoy your festive wreath!