My own professional experience has led me to believe that baklava must surely have developed out of the technique of rolling thin dough. The authoritative Larousse Gastronomique explains that this technique, under the name of ‘strudel’, appeared in the Austro-Hungarian Empire during the Ottoman period.

THE SECRET LIES IN THE THINNESS OF THE DOUGH
But who invented the technique of rolling thin dough? Due to their nomadic lifestyle, the Turks of Central Asia carried their cooking equipment with them on horseback. The only stove that can be carried on the back of a horse is a thin metal brazier, and the food prepared on such a brazier has to be thin too so that it will cook quickly. The technique of rolling fine dough, which was born of the exigencies of nomadic life, would develop eventually into baklava. The baklava unique to the Middle East and Eastern Mediterranean today is compared in some sources to ‘strudel’ or ‘yufka’ (Greek phylo leaves).