Baklava is rich Turkish, Greek, and Middle Eastern pastry. Phyllo is a simple flour-and-water dough that is stretched to paper thinness and cut into sheets, a process so exacting that it is frequently left to commercial manufacturers. For baklava, 30 or 40 sheets of phyllo, each brushed liberally with melted butter, are layered in a baking pan with finely chopped walnuts, pistachios.