At this point, most avid New Orleans diners know two things about Shaya: that the cuisine is Israeli, though we have little local precedent for what that might mean; and that it’s been fiercely popular, to a degree rarely sustained this long.

Just last week, the crowded host station here resembled an airline ticket counter as prospective diners without reservations angled for the equivalent of standby status. This was at lunch, at a restaurant that’s been open eight months and in a city teeming with new options.

For those who haven’t dined here, there may be something mysterious to the clamor for a cuisine that, on its face, relates so closely to what’s available at much lower prices at so many Middle Eastern cafes across town. Any meal at Shaya is built around pita bread, just about everyone gets hummus (served five ways) and labneh, tabouleh, falafel and lamb kebabs appear across the menu.

But no one in New Orleans is cooking Middle Eastern food like this, and the key difference isn’t anything revolutionary, nor does it feel flash in the pan.

Rather, it’s the way chef Alon Shaya has mastered the elegant simplicity of the region’s flavors, expressing them fully and with a sharp eye for detail. And it’s the way his restaurant, another in the Besh Restaurant Group’s portfolio, presents them in a style well synched to the way so many people want to eat today.

Dishes are straightforward and flavors are under-manipulated, enhanced with small but essential touches (fresh herbs, a dappling of zaatar or a pulse of spicy harissa). And meals are ideally arrayed for a shared, small plates format. This follows the tradition of mezze, a parallel to tapas with deep roots in the Middle East. It also happens to be right in step with the times.

The Israeli identity is crucial, bringing us dishes from both historic regional cooking and the cultural interplay that’s accelerated there since the creation of the modern Israeli state. Shaya, a native of Tel Aviv, thus can draw both from staple Middle Eastern flavors and influences from the broad Jewish diaspora now brought back to the homeland.

Shaya is the place to taste the Lebanese classic kibbeh nayah, a tartare here mixing raw grassy-flavored lamb and beef with bulgur, bits of mint and a trace of pomegranate sweetness. Persian rice is another standout, though an unlikely one, sounding like a humble side starch but yielding a buttery, delicious flavor under its molded crust of browned grains.

The aromatic tang of curried yogurt and flavors of sesame, cumin and oregano accentuate the juice-packed, crisp-skinned roasted chicken. For local palates, the shrimp shakshouka may bring shrimp Creole to mind with its warm tomato and sweet pepper flavors between the poached eggs and bright, pesto-like sauce. The shrimp also underscores that Shaya is not in any way kosher.

Mezze arrive on pounded metal trays like clustered cameos. A few examples: orbs of watermelon and rich feta, resembling an eastern version of a Caprese salad; ikra, a creamy dip with tiny black roe; lutenitsa, a chunky red pepper and eggplant purree; shipka peppers, narrow, glistening vessels piped with goat cheese like Spanish piquillos.

Just about any dish is fodder for the pita, which is baked in a wood-fired oven that makes all the difference. Toasty and malty tasting, with a faint lace of char against the pillow-soft interior texture, it’s puffed up with steamy bakery air captured within its shell.

At lunch, entrees give way to sandwiches, which puts another angle on the Israeli experience Shaya can bring to the table. The Jerusalem mixed grill, a funk fest of griddled chicken hearts and livers common to the street stands of its namesake city, gets an added richness from sweetbreads, all tumbling out of a pita. The chicken schnitzel is more approachable, built on sesame-crusted challah, layered with thick pickles and spicy with harissa mayonnaise.

Desserts keep the regional flavors coming, with an aptly named “milk and honey” cheesecake made from labneh and the beautifully rendered malabi, which corresponds to panna cotta.

Such a curated dessert menu joins the deep and well-pitched wine list as hallmarks of the Besh brand. So too is all the buzz that attended Shaya even before it opened, and has circled it ever since, and that can’t be discounted in the story of its runaway success thus far. This restaurant did not exactly appear out of nowhere.

But if Shaya has been flying high, dining here shows the character and quality built into the operation and the heart and soul put into the food, and that feels like a bedrock foundation.

Follow Ian McNulty on Twitter @IanMcNultyNOLA.