The Greek-style dessert made with shredded phyllo dough, nuts, and syrup is kataifi. The name can refer to the fine, thread-like pastry itself or to sweets made by baking or frying those strands with nuts and sweet syrup.
Kataifi pastry resembles delicate vermicelli. It is produced by pouring a thin flour-and-water batter through tiny openings onto a heated rotating griddle, creating hair-like strands. These strands are sold fresh, refrigerated, or frozen, then shaped into pastries or layered in trays.
A typical dessert preparation combines the pastry with chopped walnuts or other nuts, butter, and a sugar syrup. The finished pastry is baked or fried until crisp, then soaked so the syrup penetrates the strands while preserving some crunch.
The word is also used in a broader Middle Eastern food tradition. Kadayif and kataifi are related names derived through Ottoman Turkish from Arabic qaṭāʾif. This is why the same pastry family appears in foods such as Turkish tel kadayıf and knafeh. It is distinct from baklava, whose main structure is layered sheets of whole phyllo rather than fine pastry threads.