1. Preheat the oven to 392°F or 200°C.

2. Line a baking sheet with parchment paper.

3. In a large mixing bowl combine the flour, vanilla sugar, cardamom, and salt and mix until well combined.

4. Add the cold butter and mix until the dough comes together.

5. Add the cold water a little at a time until the dough forms a ball.

6. Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.

7. Roll out the dough to a rectangle about 1/2 inch or 1 cm thick.

8. Spread softened butter over the dough leaving a 1-inch or 2.5 cm border around the edges.

9. Sprinkle with granulated sugar and cinnamon.

10. Roll the dough into a log starting from the long side.

11. Cut into 1-inch or 2.5 cm thick slices.

12. Place the slices on the prepared baking sheet leaving about 1 inch or 2.5 cm of space between each bun.

13. Brush the tops with beaten egg and sprinkle with granulated sugar.

14. Bake in the preheated oven for 18-20 minutes or until golden brown.

15. Allow to cool before serving.