Melt the butter in a saucepan over medium heat for about 3 minutes. Let it brown lightly for 1-2 minutes more, then remove from heat. Cool to warm temperature for about 5 minutes. In a bowl, stir together the warm butter with the sugar, salt, and vanilla sugar until creamy. Add the flour one tablespoon at a time, stirring after each addition.
Shape the dough into rolls immediately (use cling film to help prevent sticking if needed). Refrigerate for 12-14 hours.
Cut the chilled dough into slices and place on an ungreased baking tray. Bake at 170°C (338°F) for 20-25 minutes.