Combine all dough ingredients in a mixing bowl and knead 10 minutes until smooth and elastic. Place in a lightly oiled bowl, cover with plastic wrap, and let rise for 1 1⁄2 hours at room temperature or overnight in the refrigerator.
Prepare sugar syrup by dissolving sugar in boiling water. Chill until ready to use.
Roll the dough into a thin rectangle on a lightly floured surface. Spread the melted white chocolate with butter evenly, then layer halva and sprinkle chopped white chocolate and a little halva.
Roll the dough into a log and freeze for 20 minutes to make it easier to handle. Cut the log lengthwise and braid the two halves. Transfer to a baking pan or place free-form on a tray. Cover and let rise for 30 minutes.
Brush the cake with beaten egg and bake in a preheated convection oven at 330°F/165°C for 35 minutes.
Immediately brush the warm cake with cold sugar syrup. Let set, then optionally sprinkle halva threads on top.