I first heard the expression “winged nostrils” from an Italian chef who was showing me how to roast a pigeon. It was his term for a chef's instinctive olfactory understanding of when a particular dish is done.

Recently I heard an almost identical turn of phrase while attending an outdoor cooking demonstration in a small Turkish village not far from Izmir. The cook was showing me how to prepare a local dish called peynirli bogaca—a. traditional hearth bread made with two unleavened olive-oil bread sheets stuffed with a fast-melting cheese called kesik and some chopped parsley. The bread is assembled in an oiled clay dish set over olive-wood embers, covered with a flat iron lid, then topped with more hot embers. It bakes quickly. “Your nose will tell you when it's done,” the Turkish cook advised.

There came a certain point during the cooking when, indeed, the aroma changed. One instant I smelled baking bread, the next a finished dish—a wonderful and unusual nutty aromatic blend of sesame and cheese. I nodded at the cook. She smiled and nodded back, then quickly removed the bread from the clay dish.

It was wonderful! The hot, slightly burned, crunchy sandwich had a wafer-thin crisp bottom, a crackly top, and a marvelous luscious, oozing, bubbling cheese filling. At her suggestion I drank a glass of ayran, yogurt mixed with cold water, as an accompaniment.

This Turkish flatbread, which is almost identical to a Genoese flatbread called focaccia colformaggio di Recco, is just one of many flaky hearth breads found in different guises around the Mediterranean. (Also similar are the French fouace, the Bulgarian pogacha, and the Algerian bourak b'l-djbene.) Please don't confuse this with the much better known, puffy, yeast-based Italian focaccia, which is served at room temperature. The Genoese focaccia is made without yeast and is always served hot from the hearth.

Another variation, using this same particular pastry and method, is a wonderful torta from the Ligurian-Tuscan coast made with greens and squash, and on the Black Sea a delicious bread pie filled with buffalo-milk mozzarella and feta served hot.

Long ago all these breads were baked in the fireplace. A clay flat-rimmed pan, called a cerepene in Turkey and testo in Italy, was thrust into the coals, then more coals were piled on top, imbuing the dough with a smoky flavor.

My versions are easily baked on a pizza pan on a preheated stone in a hot oven. Please be sure not to open the oven door while they cook, lest you reduce the intense heat. There is no need to check to see how the breads look; your “winged nostrils” will tell you when they're done.

The quick-to-make dough needs to rest overnight, so plan accordingly