Anxiety was in the air this August when, after almost 20 years, Periyali closed for renovations. True, the groundbreaking Greek taverna had fallen behind the times. New Greek restaurants like Onera and Parea have sprung up, offering inventive twists on the cuisine, while Periyali stuck to the same old formulaic souvlaki and moussaka. But the formula was the best in town — was Periyali planning to radically reinvent it for the 21st century? Sitting in the freshly reopened restaurant for the first time, perusing the menu at the shiny new marble-topped bar, I felt a sweeping sense of relief. Only the details — skylights, a bright mural, fresh upholstery — are new. The reliable food and the charming mood are as old-fashioned as ever.

The charcoal grill still leaves its smoky kiss on a wine-marinated octopus starter ($14), whose supple, briny tang lingers in fond memory for weeks; as well as on faintly modern treats like a plate of olive-oily oyster mushrooms ($14), with just as much chew but an earthier savor. For earthiness, though, nothing can beat the sautéed chicken livers ($10), which are complemented by a brothy, oniony bed of lentils.

Fried calamari is almost as ubiquitous on New York menus as tires are on New York taxis, and often just as tasty. In a nuevo-Latino restaurant, you can dip the familiar rings in chipotle; in a pan-Asian place, the dip will have ginger. I don’t know that every calamari appetizer can trace its parentage to Greece by way of Periyali, but the version here ($10) is the Platonic ideal: pale gold and crisp, but never letting the batter distract from the delicately firm meat of the matter. They’re full of flavor, with or without the lemony, garlicky puree. The same sauce invigorates a plate of broad beans ($10), cooked till they’re bursting, rich, and tender. The restaurant’s tzatziki and taramosalata are just as accomplished, with subtle balance, not the blasts of garlic and salt that often typify those dips.

Lamb in various forms dominates the main courses, as indeed it should. Three charcoal- and rosemary-perfumed chops ($29) have assertive flavor, and a texture that’s firmer than most, with a clear distinction between its salty surface and yielding interior. The scent evokes a Greece of mountainside herbs, open fires, and the propitiation of gods. The shank of the same beast ($26) has an entirely different personality, braised for a comforting, wintery effect, its abundance of long-cooked, darkly savory meat clinging to a big bone with the most tenuous of grasps. It’s surrounded by tomatoey stewed orzo with an acidic tinge that neatly draws out the lamb’s flavor. The classic moussaka sandwiches (just $18) ground lamb browned with tomato between juicy black eggplant strips below and fluffy pale béchamel on top. The combination is unstoppable.

Fish, a specialty at many restaurants that serve this island cuisine, is not prevalent at Periyali, apart from a daily charcoal-grilled whole one, and the salmon exohiko ($27). In the latter, a filet of the fish is rolled with feta cheese in a big, crispy pie of phyllo. The golden-brown, buttery outside contrasts pleasingly with the fresh moistness of the fish, but the dish’s flavor is quite subdued compared to the menu’s peaks. The chef, Thomas Xanthopoulos, makes his souvlaki ($28) with filet mignon, a refinement that works excellently. The skewered beef takes on flavors of lemon and smoke, while retaining a tender succulence that the traditional pork never has.

After the hefty, meaty meal, when the waiter brings over a dessert platter laden with honeyed cakes ($8 each), the invitation feels like an imposition. Who would want to pile on more food at this point? Those (like me) who are compelled to do so will find themselves rewarded. The kadaifi is the best dessert I’ve had in recent memory. Fine shreds of toasted dough form a nest that’s soaked with cinnamon-tinged syrup, studded with walnuts, and topped with lemon-scented custard and cream, for a rich, refreshing balance of flavors and consistencies. Periyali’s popular baklava is not particularly exceptional, but the thick rice pudding — practically just cream thickened with a little rice — stands out.

When Periyali opened in 1987, its upscale Greek offerings were a rarity in the city. Its half-Greek, half-barbarian wine list was novel. Retsinas, like Periyali’s $14 half-bottle of Malamatina — whose, dry, aromatic appeal complements herbal flavors in the food — were the extent of Greek wine in New York. In 2006, varietals like agiorgitiko and xinomavro can be found around the city without looking too hard, and upscale Greek restaurants are popular enough to constitute a trend. But among all the innovation, comfort, attention to detail, and true deliciousness are still rare. As its many regular customers know, with or without its facelift, Periyali has aged gracefully from a groundbreaker into a landmark.

Periyali (35 W. 20th St., between Fifth and Sixth avenues, 212-463-7890).